Calculus problems?

Question

I have two questions I'm absolutely stuck on. Any help would be much appreciated!!

1. Find the slope of the tangent line at the point P
y = a^2 / (a^2+x^2) .... P(a, 1/2)

and this next one is going to be challenging to type...

2. What is the value of:
http://i179.photobucket.com/albums/w293/controldeficit/calculus.gif
(since I couldn't type that out).

Answer 1

1. Find the slope of the tangent line at the point P
y = a^2 / (a^2+x^2) .... P(a, 1/2)

Treat 'a' as a constant. First find y ', then evaluate that expression at 'a', whenver you see an x

y ' = -2xa^2 / (a^2+x^2)^2
y ' | (x = a) = -2(a)a^2 / (a^2+a^2)^2
= -2a^3 / 4a^4
= -1/2a

2. What is the value of:
Expand the numerator, collect like terms, cancel. Then take the limit by direct substitution and evaluate at x = 3. I'll use an 'h' instead of your 'delta x'

[2(x+h)^2 - 2x^2] / h
= [2(x^2 + 2xh + h^2) - 2x^2] / h
= (2x^2 + 4xh + 2h^2 - 2x^2) / h
= (4xh + 2h^2) / h
= 4x + 2h

Now, lim h ---> 0

= 4x

Now, evaluate at x = 3

= 4(3)
= 12

Answer 2

y = a^2 / (a^2+x^2)
y' = -a^2(2x)/(a^2+x^2)^2
When x=a, y' = -2a^3/(4a^4) = -1/2a = slope

This looks like you are trying to find the derivative of 2x^2.
Your limit will turn out to be 4x.
When x=s, the derivative = 4*3 = 12

Answer 3

poor you sorry i cant help i dont take calc until next year thank god but i would if i could