(a). Show that the function f (x) = ln (x + √x2 + 1) is an odd function. (b). Find the inverse function of f.
> Express the given quantity as a single logarithm. ln 5 + 5 ln 3
> Find the exact value of each expression. (a). e-2ln 5 (b). ln (ln ee10)
> Derive Equations 1 for the case π/2 < θ < π.
> Find the exact value of each expression. (a). ln (1/e) (b). log10 √10
> Find the exact value of each expression. (a). log5 125 (b). log3 (1/27)
> (a). What is the natural logarithm? (b). What is the common logarithm? (c). Sketch the graphs of the natural logarithm function and the natural exponential function with a common set of axes.
> (a). How is the logarithmic function y = logax defined? (b). What is the domain of this function? (c). What is the range of this function? (d). Sketch the general shape of the graph of the function if y = logax a > 1.
> (a). Find parametric equations for the ellipse x2/a2 + y2/b2 = 1. [Hint: Modify the equations of the circle in Example 2.] (b). Use these parametric equations to graph the ellipse when a = 3 and b = 1, 2, 4, and 8. (c). How does the shape of the ellipse
> Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3. Figures 3: Figures 13: y = 10x+2 y4 10 4" 1.5 1 y y = e* m=1
> Use the given graph of f to sketch the graph of f-1. yA 1 2
> Describe the motion of a particle with position (x, y) as varies in the given interval. x= sin t, y = cos't, , -27sts 2m
> Use the given graph of f to sketch the graph of f-1. -1 1/
> Find an explicit formula for f-1 and use it to graph f-1, f and the line y = x on the same screen. To check your work, see whether the graphs of f and f-1 are reflections about the line. f (x) = 2 - ex
> Graph the curve x = y – 2sin πy.
> Find a formula for the inverse of the function. y = ex/1 + 2ex
> Find a formula for the inverse of the function. y = ln (x + 3)
> Find a formula for the inverse of the function. y = x2 – x, x > 1/2
> Find a formula for the inverse of the function. f (x) = e2x-1
> Find a formula for the inverse of the function. f (x) = 4x – 1/2x + 3
> Suppose a curve is given by the parametric equations x = f (t), y = g (t), where the range of f is [1,4] and the range of g is [2, 3]. What can you say about the curve?
> In the theory of relativity, the mass of a particle with speed v is where m0 is the rest mass of the particle and is the speed of light in a vacuum. Find the inverse function of f and explain its meaning. mo m = f(u) = VI - v/c²
> Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3. Figures 3: Figures 13: y = 2 (1 – ex) y4 10 4" 1.5
> Describe the motion of a particle with position (x, y) as varies in the given interval. x = 5 sin t, y = 2 cos t, -TsI< 57
> Describe the motion of a particle with position (x, y) as varies in the given interval. x= 2 sin t, y = 4 + cos t, 0st<37/2
> If g (x) = 3 + x + ex, find g-1(4).
> (a). Eliminate the parameter to find a Cartesian equation of the curve. (b). Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x= In t, y = Vī,
> (a). Eliminate the parameter to find a Cartesian equation of the curve. (b). Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x= sin 0, y = cos 20
> (a). Eliminate the parameter to find a Cartesian equation of the curve. (b). Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x = e' – 1, y = e2"
> (a). Eliminate the parameter to find a Cartesian equation of the curve. (b). Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x = e", y =t + 1
> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. g (x) = cos x
> (a). Eliminate the parameter to find a Cartesian equation of the curve. (b). Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x= sin t, y = csc t, 0<t<T/2
> (a). Eliminate the parameter to find a Cartesian equation of the curve. (b). Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x = cos 0, y = 2 sin 0, 0< 0 <
> The graph of f is given. (a). Why is f one-to-one? (b). What are the domain and range of f-1? (c). What is the value of f-1 (2)? (d). Estimate the value of f-1 (0). 이 1
> (a). Eliminate the parameter to find a Cartesian equation of the curve. (b). Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x= sin 0, y = cos- 30,
> (a). Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b). Eliminate the parameter to find a Cartesian equation of the curve. x= t?, y =t
> (a). Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b). Eliminate the parameter to find a Cartesian equation of the curve. x= Vf, y=1 - t
> (a). Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b). Eliminate the parameter to find a Cartesian equation of the curve. x=1+ 3t, y= 2 – t?
> If the circle C rolls on the outside of the fixed circle, the curve traced out by P is called an epicycloid. Find parametric equations for the epicycloid.
> Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as increases. x= e + t, y = et – t, -2 < t<2
> Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as increases. x = cos't, y = 1 – sin t, 0 <ts 7/2 %3D
> Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as increases. x = t?, y=t - 4t, -3 <t<3
> A hypocycloid is a curve traced out by a fixed point P on a circle C of radius b as C rolls on the inside of a circle with center O and radius a. Show that if the initial position of P is (a, 0) and the parameter θ is chosen as in the figure
> Draw the graph of the equation x4 – 4x2 – x2y2 + 4y2 = 0.
> Describe the motion of a particle with position (x, y) as varies in the given interval. x = 3 + 2 cos t, y=1 + 2 sin t, /2 <t< 3m/2
> Sketch the graph of the function g (x) = |x2 – 1| - |x2 – 4|.
> Sketch the graph of the function f (x) = |x2 – 4| x| + 3|.
> The altitude perpendicular to the hypotenuse of a right triangle is 12 cm. Express the length of the hypotenuse as a function of the perimeter.
> If f0 (x) = x2 and fn+1 (x) = f0 (fn (x)) for n = 0, 1, 2, …, find a formula for fn (x).
> Solve the inequality ln (x2 – 2x - 2) < 0.
> Evaluate (log23) (log34) (log45) …(log3132).
> One of the legs of a right triangle has length 4 cm. Express the length of the altitude perpendicular to the hypotenuse as a function of the length of the hypotenuse.
> Find the domain and range of the function. Write your answer in interval notation. F (t) = 3 + cos 2t
> Find the domain and range of the function. Write your answer in interval notation. h (x) = ln (x + 6)
> If f (x) = x5 + x3 + x, find f-1 (3) and f (f-1(2)).
> Find the domain and range of the function. Write your answer in interval notation. g (x) = √16 – x2
> Find the domain and range of the function. Write your answer in interval notation. f (x) = 2/ (3x – 1)
> Sketch a rough graph of the yield of a crop as a function of the amount of fertilizer used.
> Use parametric equations to graph the function f (x) = 2x + ln x and its inverse function on the same screen.
> (a). Sketch the curve represented by the parametric equations x = et, y = √t, 0 < t < 1, and indicate with an arrow the direction in which the curve is traced as increases. (b). Eliminate the parameter to find a Cartesian equation of the curve.
> Graph the three functions y = xa, y = ax, and y = logax on the same screen for two or three values of a > 1. For large values of x, which of these functions has the largest values and which has the smallest values?
> If f (x) = x2 -2x + 3, evaluate the difference quotient f (a + h) – f (a)/ h.
> The population of a certain species in a limited environment with initial population 100 and carrying capacity 1000 is where is measured in years. P (t) = 100,000/100 + 900e-t (a). Graph this function and estimate how long it takes for the population to
> The half-life of palladium-100, 100Pd, is four days. (So, half of any given quantity of 100Pd will disintegrate in four days.) The initial mass of a sample is one gram. (a). Find the mass that remains after 16 days. (b). Find the mass m (t) that remains
> Solve each equation for x. (a). ex = 5 (b). ln x = 2 (c). eex = 2
> Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3. Figures 3: Figures 13: y = 1 – 1/2 e-x y4 10 4" 1.5
> Find the exact value of each expression. (a). e2ln3 (b). log 1025 + log104
> Find the inverse function of f (x) = x + 1/2x + 1.
> If f (x) = 2x + ln x, find f-1 (2).
> Express the function F (x) = 1 /√x + √x as a composition of three functions.
> If f (x) = ln x and g (x) = x2 - 9, find the functions (a) f0g, (b) g0f, (c) f0f, (d) g0g, and their domains.
> Use transformations to sketch the graph of the function. if x<0 f(x) = ez – 1 if x> 0
> Use transformations to sketch the graph of the function. f (x) = 1/ x + 2
> Use transformations to sketch the graph of the function. y = 2 - √x
> Use transformations to sketch the graph of the function. y = 1/2 (1 + ex)
> Use transformations to sketch the graph of the function. y = 3 ln (x – 2)
> Give an example of each type of function. (a). Linear function (b). Power function (c). Exponential function (d). Quadratic function (e). Polynomial of degree 5 (f). Rational function
> Discuss four ways of representing a function. Illustrate your discussion with examples.
> How to make an article, in Word with columns and pictures.
> Write an application in Java that reads a line of text and prints a table indicating the number of one-letter words, two-letter words, three-letter words, and so on, appearing in the text.
> Write a program that reads a line of text, changes each uppercase letter to lowercase, and places each letter in a queue. The program should then verify whether the line of text is a palindrome.
> Trace the following Code. An ASCII Chart is provided below the question. def letterfun ( text): res="" for letter in text: if letter >= "A" and letter <= "Z": x = ord(letter)-65 x = (x + 15) % 26 x = chr(x+65) res+-x print (" Replaced" , letter ,"w
> Write a C++ program that reads input from a text file and counts the number of characters read from the input. If the character read is a letter ('a'-'z'), counts the number of times that letter occurs [using an array] (both uppercase and lowercase shoul
> _______ is breaking down an object into parts, hiding and protecting its essential information, and supplying an interface to modify the information in a controlled and useful manner.
> I have been struggling with the following coding assignment 3. 2. Challenge Content concatenation Evaluate your content concatenation skills by completing the following tasks: Append the current user to the ~/workspace/project-log/changelog.txt file: Cha
> Challenge Changing file permissions Evaluate your chmod command understanding by completing the following tasks: Changing file permissions Evaluate your chmod command understanding by completing the following tasks: 1. List visible and hidden file
> PROJECT STEPS You work for All Around Outside Maintenance, an outdoor maintenance 1. company, and have decided to create an Access database to make it easier to keep track of business information. In this project, you will create and update tables, impo
> Write a function that computes and return the frequency of letters in a given text file that is to compute the frequency of occurrence of each letter in the alphabet. Write a function that computes and return the frequency of letters as the first letter
> Can someone code this is Python 3 or Codio please. 6. Regular Expression Search Challenge In this challenge you will use the file regex_search_challenge_student.py to: Regular Expression Search Challenge Using the Python string below to perform a search
> Codio (python) Challenge X factorial, also written as X!, is X*(X-1) * (X-2) * (X-3).........* (1) So, 4! is 4*3*2*1 = 24 We provide you with a value N. Calculate N! and output only the final result. #Get N from the command line import sys N = int(sys.ar
> 5. 6. Final challenge For your final challenge in this unit, you will load two files. The first file F1 will have information about some accounts. It will be pipe-delimited and have one record per line, with these fields: ACCOUNT NUMBER | PIN CODE | BA
> 26. A(n) _______ is an abstract data type that stores and retrieves items in a last-in-first-out manner. queue stack vector array None of the above Quèstion 28 The pre order traversal of the tree shown below is: (100 19 36 (17 3 (25 1 7 100,19
> What would happen if we add cout to the end of the program (when s2 is empty?) Fix Stack.h so that these problems would not occur. #ifndef STACK_H #define STACK_H // your name // Stack.h // date // description #include <vector> using namespace std;
> Suppose we have a vector of integer stacks: vector sv; Write a function to return the number of stacks in the vector that are not empty.
> I made a program for class to find the amplitude of oscillation for our problem but I cannot figure out how to graph the comparison of amplitude. Basically our given is: Ka= input (Stiffness of board A); Ma= input (Weight of board A); Kb= input (Stiffnes
> Predict the products of the reaction below. Draw a mechanism. 3. 4. HO H;SO, heat Br NaOEt iPr
> Describe governance principles, standards, and practices in the IT environment. Using the media presentation as a case study: Describe the role of an organization's IRB. Describe the role of an organization's technology PMO. List and describe the compone
> HIPAA specifically addresses health care organization's use of social media platforms. True False
> Create a program that accepts and formats a paragraph from the user as follows: Ask the user for the length of the paragraph in characters. Repeatedly ask the user for the number of characters and only except a number more than 80 and less than 500. Cr
> PYTHON Write code that attempts to read a number from the console. Your code will read a string and then attempt to convert that string into a float. Your code will start out with: userInput = input ("Please type a real number: ") And then your code wi
> 1. Explain why an organization's firewall should block incoming packets the destination address of which is the organization's broadcast address. 2. Explain why an organization's firewall should block outgoing packets the source addresses of which are n
