Calculus Answers

Is the graph of y=sin(x5) increasing or decreasing when x=13?
(enter increasing, decreasing, or neither).

Is it concave up or concave down?

Let p(x)=ax3−x, where a is constant and a>0.

Find the local maxima and minima of p.
(Enter your maxima and minima as comma-separated xvalue,classification pairs. For example, if you found that x=−2 was a local minimum and x=3 was a local maximum, you should enter (-2,min), (3,max). If there were no maximum, you must drop the parentheses and enter -2,min.)

maxima and minima:

Is every onto strictly decreasing function invertible? Justify your answer.

Examine the function,
f(x)=2x^3- 9x^2- 60x+150
for extreme values.

Show that the sequence {fn}of functions, where

fn (x )=n/(x+2n)
is uniformly
convergent in [0.k] where k > 0.

The area of a square with side s is A(s)=s2. What is the rate of change of the area of a square with respect to its side length when s=8?

Check whether the function f given by



f(x)=1/(2x-4)^2 ∀x∈]-2,2[

Is continuous in the interaval ]-2,2[.is it bounded?justify your answer.

If f(x)=8x+10, find the instantaneous rate of change of f(x) at x=8

Check whether the function, ,f defined below, is uniformly continuous or not:

f(x)=x^(1/2), x∈[1,2]

Use Lagrange’s mean value theorem to prove that


x-x^2/2《log(1+x)《x-x^2/2(1+x) if x》0.