Calculus Answers

The equation of motion of a particle is s =((t^3)-3t) where s is in metres and t is in
seconds. Find
i) the velocity and acceleration as functions of t,
ii) the acceleration after 2 seconds,
iii) the acceleration, when the velocity is 0.

Evaluate the limit, if it exists. If not, enter "n" below.
limh→0
(2+h)^3 −8
--------------
h
(the whole thing is divided by h)

A) Let f(x)=4−x^2 if x≤6 and x−1 if x>6
Find each of the following limits. If the limit does not exist, enter DNE below.
limx→6−f(x)=
limx→6+f(x)=
limx→6f(x)=

Which of the following statements are true, and which are false? Give reasons for
your answers in the form of a short proof or a counterexample.
i) There are at least two ways of describing the set ...},8,7{ .
ii) Any function with domain R×R is a binary operation.
iii) The graph of every function from ]1,0[ to R is infinite.
iv) The function :f R → R , defined by = xx)x(f , is an odd function.
v) The domain of the function ,gf o where = x)x(f and −= ,x2)x(g is ]2

Differentiate the following with respect to x

e^x log x/ x+1

Differentiate the following with respect to x

e^x/log x

Differentiate x^20 +2x -10 from first principle

Use Z substitution
I= ∫ dx /(1+sinx)

I= ∫ ( y /(√((2y^2)+1)) )dy

1) ∫ x^4/x^10+100 dx
2) ∫ √x+9/x dx
3) ∫ dx/1+2e^x – e^-x
4) ∫ 2x^2dx/√9-x^2