Calculus I Exam 1 Review Questions

ESP Calculus I Exam 1 Review Questions

Find an equation for the function graphed below:
Try to find the equation of a single function s(t) , which will denote the height of an object in feet after t seconds, which has all of the following properties simultaneously:
- The average velocity found using s(t) between the times of t = 3 and t = 5 is about -1/2.
- The instantaneous velocity found using s(t) at t = 3 is about 2.
- The instantaneous velocity found using s(t) at t = 5 is about -3.
- The maximum height of the object is about 5 ft.
Hint: Try drawing the graph of such a thing first, then try to find the equation of something like it.
Try drawing a single function y = f(x) which has the following properties simultaneously:
- The function values y = f(x) exists everywhere, except at x = -1, x = 1, and x = 4.
- The limit exists everywhere, except at a = -1, and a = 4.
- The function is continuous everywhere, except at x = -1, x = 1, x = 3 and x = 4.
- f(x) is negative only when 0 < x < 1.5, and when x > 4
- The limit
- The limit
- The limit
- The limit
True or False: If the limit , then f(2) = 3.
For the function s(t) = -t² + 10t, find the slope of the tangent line to the graph when t = 1, by finding an expression for the slope of the secant line between the two points where t = 1 and t = 1+h, then letting h shrink to 0.