Calculus help plz?

Question

I've been working on 100 calculus problems for 3 hours and i cant figure these out, could someone plz help me?


1. find the vertical asymptotes of (x+1)/( x^2-1) ?

2. f(x) decreases w/out bound as x approaches what value from the right?
f(x)= 9/ [(x-4)(9-x)]

3. if f(2)=3 and f'(2)=-1, find an equation of the tangent line when x=2

4. find the point(s) on the graph of the function f(x)= x^3-2 where the slope is 3

5. Let f(3)=0, f'(3)=6, g(3)=1 and g'(3)=1/3 . Find h'(3) if
h(x)=f(x)/g(x)

6.Find the equation of the to the graph of f(x)=x*sin(x) when x=0

7. Find all critical numbers for the function f(x)= (9-x^2)^(3/5)

8. Find the absolute maximum and absolute minimum of f on the intreval (-1,2]

9. Find all open intrevals on which f(x)= x/(x^2+x-2) is decreasing

10. Find all the points of inflection of the graph of the function
f(x)= x^4+x^3

11.Find all the horizontal asymptotes for f(x)= 5x / sqrt(x^2+3)

Answer 1

....it is unlikely for you to work 100 questions and skip the first 11 questions. Either you lied to us and expected sympathy or you were just too lazy to do your own homework. If you could do the rest of the homework, why skip these problems? your homeworks must be similar to each other. Plus... the first question is a pre-cal question.

Answer 2

Here's help with 1:
(x+1)/(x^2-1) = (x+1)/[(x+1)(x-1)]
= 1/(x-1)
which has a vertical asymptote at x = 1

For 2, the ovbious answer is either going to be 4 or 9, and to figure this out, you need to decide whether x is a tiny bit more than 4, whether the answer is a little bit more or less than if x is just a bit greater. Well, consider 4.2 and 4.3 for values of x. f(4.2) =
9/[(.2)(9-4.2)]
f(4.3) = 9/[(.3)(9-4.3)]
the first term (.3 and .2) in the denominators
clearly changing faster than the second terms, but clearly the function is INCREASING as x gets closer to 4 from the right.
You can go through the same exercise with x=9, and you will see that this satisfies the question.