Derivatives: Finding a dervative, with a given cordinate

Find an equation of the tangent line to the at the given point (1,1)

y= squareroot( x)

What I tried to do:

Lim __ f(x) - (a)__ -> lim __square root (x) - (1)__

x->a x-a x->1 (x)-1

I don't know what to do because there is an answer, and what I tried to do makes it 0/0 which is bad.(Thinking)

Re: Derivatives: Finding a dervative, with a given cordinate

Quote:

Originally Posted by

**SaltyBriefs** Find an equation of the tangent line to the at the given point (1,1)

y= squareroot( x)

What I tried to do:

Lim __ f(x) - f(a)__ -> lim __square root (x) - (1)__

x->a x-a x->1 (x)-1

correction

$\displaystyle f'(1) = \lim_{x \to 1} \frac{\sqrt{x} - \sqrt{1}}{x - 1}$

$\displaystyle f'(1) = \lim_{x \to 1} \frac{\sqrt{x} - 1}{x - 1}$

$\displaystyle f'(1) = \lim_{x \to 1} \frac{\sqrt{x} - 1}{(\sqrt{x} - 1)(\sqrt{x} + 1)}$

finish it?