Evaluate the following limits:
A) lim x^2+10x-39/x-3
x to 3

B) Lim x-2/(squareroot of x+2)-2
x to 2

C) lim 2x^2-5x+3/5x^2-6
x to infinity

Problem 2
Desribe or sketch an example where a function is continuous but not differentiable. Explain why it is continuous but not differentiable..

2. Originally Posted by vc15ao4
Evaluate the following limits:
A) lim x^2+10x-39/x-3
x to 3
Factor,
x^2+10x-39=(x-3)(x+13)

B) Lim x-2/(squareroot of x+2)-2
x to 2
x - 2 = (x+2) - 4
Difference of two squares,
[sqrt(x+2) - 2 ]*[sqrt(x+2) + 2]
Now cancel numerator and denominator.

C) lim 2x^2-5x+3/5x^2-6
x to infinity
Divide numerator and denominator by x^2

(2 - 5/x + 3/x^2)/ (5 - 6/x^2)

As x---> BIG

We have,

(2-0+0)/(5-0)

3. Originally Posted by vc15ao4
Problem 2
Desribe or sketch an example where a function is continuous but not differentiable. Explain why it is continuous but not differentiable..
Consider the function f(x) = |x|.

This function is continous because |x| = sqrt(x^2) and both x^2 and sqrt(x) are continous so if there composition.

But it is not differenciable.

4. Originally Posted by vc15ao4
Evaluate the following limits:
A) lim x^2+10x-39/x-3
x to 3

B) Lim x-2/(squareroot of x+2)-2
x to 2

C) lim 2x^2-5x+3/5x^2-6
x to infinity
Here

EDIT: you're too quick for me TPH! I was going to use that example for the second problem as well
I approached B) a different way, but your way seems nicer