2.99 See Answer

Question: Find the exact value of each expression. (


Find the exact value of each expression.
(a). e2ln3
(b). log 1025 + log104


> 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 &Icirc;&cedil; 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.

> (a). Show that the function f (x) = ln (x + √x2 + 1) is an odd function. (b). Find the inverse function of f.

> 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 &acirc;&#128;&#147; 1/2 e-x y4 10 4" 1.5

> 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

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> 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

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See Answer