Calculus Answers

Differentiate the following function:
u=t2−−√3−6t3−−√
u′=

Suppose that f(x)=3x2−4.

(A) Find the slope of the line tangent to f(x) at x=−1.
(B) Find the instantaneous rate of change of f(x) at x=−1.
(C) Find the equation of the line tangent to f(x) at x=−1. y=

Suppose that f(x)=2/x^9. Evaluate each of the following:

f′(2) =

f′(−3) =

Suppose that f(x)=9x4/5−2x5/7. Evaluate each of the following:

f′(3) =

f′(6) =

f(x+h)−f(x)=7hx2−5hx+1h2x+4h2+7h3.
Find f′(x).

Determine whether or not the following series converges. If it converges, find its sum. ∑_(k=1)^∞▒1/7k

Find the radius of convergence for the series:
∑_(k=1)^∞▒〖-5x〗^k/(k+2)

Find its inverse
(a) g(x)=(x-1)/(3x+2)
(b) f(x)=4+ square root of (x^2+1)

120 numbers are written on the board. It is known that among all their pairwise
products there are exactly 2000 negative numbers. What is the largest number of
zeroes that could be written on the board?

Use the mean value theorem to prove 2.071 < squareroot of 4.3 < 2.075