Calculus final exam

Fifteen questions on all of Calculus. Answer all 15 to see your score. Questions are drawn from a bank of 99, so every attempt is different.

0 of 15 answered

Question 1 of 15

A drone rises so that its height after t seconds is s(t) = 5t^2 meters. What is its average velocity between t = 1 and t = 4?

Suppose lim(x->a) f(x) = 4 and lim(x->a) g(x) = -3. Using the limit laws, what is lim(x->a) [ (2f(x) - g(x)) * g(x) ]?

Find lim (x->5) (x^2 - 25)/(x - 5).

Find lim (x->3) (x^2 - 9)/(x - 3).

Find lim (x->2) (3x^2 - x + 7).

Find lim (x->infinity) (5x^2 - 2)/(4x^2 + 1).

Find lim (x->0) sin(2x)/x.

Find lim (x->0) sin(7x)/x.

Use l'Hospital's rule to find lim (x->0) (e^(4x) - 1)/x.

For what value of c is f continuous at x = 1, where f(x) = cx - 2 for x < 1 and f(x) = x^2 for x >= 1?

A ball's position is s(t) = 3t^2 metres. What is its average velocity between t = 2 and t = 5 seconds?

If f(x) = 1/x, what does the limit definition give for lim(h->0) [f(1 + h) - f(1)]/h?

Differentiate f(x) = 4x^3 - 2e^x + 5cos x.

Differentiate f(x) = 4x^3 - 2x^2 + 5.

Differentiate f(x) = 7x^2 + 3x^4 - 9.