Question

Limit Definition (Medals shall be handed out):

Use the limit definition to find the slope of the tangent line to the graph of f at the given point.

2(x^1/2) ; (4,4)

Answer 1

I don't think I remember how to do this.

Answer 2

Is f(x)=2x^1/2?

Answer 3

yes

Answer 4

https://www.khanacademy.org/math/calculus/differential-calculus/derivative_intro/v/calculus--derivatives-2--new-hd-version
If you watch that, it will help you.

Answer 5

Okay, thank you.

Answer 6

yw

Answer 7

slope of tangent at a point is the derivative of the curve at that point.
and the limit definition of derivative at point x=a is :
\(\large f'(a)=\lim \limits_{a \rightarrow h}\dfrac{f(a+h)-f(a)}{h}\)

Answer 8

here, the point has x=4, so take a=4
find f(4) and f(4+h) and plug those in the formula to evaluate the limit

Answer 9

wait sorry isn't it g -> a hartnn?

Answer 10

h*

Answer 11

no, its h->0
sorry for the typo
\(\large f'(a)=\lim \limits_{h \rightarrow 0}\dfrac{f(a+h)-f(a)}{h}\)

Answer 12

I'm sorry hartnn, but I am kind of confused by your approach