Question

lim ((x^2 + 3)-(-5^2 + 3)) / (x--5)
x->-5

Answer 1

I assume you just learnt the definition of derivative?

In which case, what does this quotient and limit look like?

Answer 2

ya so its f(x)=x^2+3 , P(-5,28)

Answer 3

Right, so this limit is the derivative of f evaluated at -5. So calculate the derivative and then evaluate it at -5

Answer 4

yes but the problem I'm having is with the algebra and the simplification of the limit

Answer 5

No, don't use the limit. Just look at this function.

What is the derivative with respect to x of x^2 ? And of 25? Hence of f(x)?

Answer 6

Or does the question ask you explicitly to evaluate the limit?

Answer 7

For the record, the derivative of f(x), f'(x) = 2x + 0 = 2x. So f'(-5) = 2.-5 = -10.

Answer 8

well I'm trying to find the slope of the tangent line

Answer 9

Yes, I know. I just gave you one way to get the answer and the answer itself.

But calculating now directly,
((x^2 + 3)-(-5^2 + 3)) / (x--5)
= (x^2 -25)/(x+5)
= (x+5)(x-5)/(x+5)
= x - 5

Hence the limit as x->-5 of ((x^2 + 3)-(-5^2 + 3)) / (x--5) is
the limit as x->-5 of (x-5)

I.e., -10.

Answer 10

oh wow thank you