Questions from General Calculus

Q: (a). What is a function? What are its domain

(a). What is a function? What are its domain and range? (b). What is the graph of a function? (c). How can you tell whether a given curve is the graph of a function?

Q: Use a graphing device to draw the graphs of hypocycloids with a

Use a graphing device to draw the graphs of hypocycloids with a positive integer and b = 1. How does the value of a affect the graph? Show that if we take a = 4, then the parametric equations of the h...

Q: Now try b = 1 and a = n/d,

Now try b = 1 and a = n/d, a fraction where n and d have no common factor. First let n = 1 and try to determine graphically the effect of the denominator d on the shape of the graph. Then let n vary w...

Q: What happens if b = 1 and is irrational? Experiment with

What happens if b = 1 and is irrational? Experiment with an irrational number like √2 or e -2. Take larger and larger values for and speculate on what would happen if we were to graph the hypocycloid...

Q: Match the parametric equations with the graphs labeled I-VI.

Match the parametric equations with the graphs labeled I-VI. Give reasons for your choices. (Do not use a graphing device.)

Q: Compare the functions f (x) = x5 and g (

Compare the functions f (x) = x5 and g (x) = 5x by graphing both functions in several viewing rectangles. Find all points of intersection of the graphs correct to one decimal place. Which function gro...

Q: Graph the curves y = x3 – 4x and x = y3

Graph the curves y = x3 – 4x and x = y3 -4y and find their points of intersection correct to one decimal place.

Q: (a). Show that the parametric equations x = x1 +

(a). Show that the parametric equations x = x1 + (x2 -x1) t y = y1 + (y2 – y1) t where 0 < t < 1, describe the line segment that joins the points p1 (x1, y1) and p2 (x2, y2). (b). Find parametric equa...

Q: Use a graphing device and the result of Exercise 29(a

Use a graphing device and the result of Exercise 29(a) to draw the triangle with vertices A (1, 1), B (4, 2), and C (1, 5). Exercise 29(a): (a). Show that the parametric equations x = x1 + (x2 -x1)...

Q: Find parametric equations for the path of a particle that moves along

Find parametric equations for the path of a particle that moves along the circle x2 + (y -1)2 = 4 in the manner described. (a). Once around clockwise, starting at (2, 1) (b). Three times around counte...