Question

use the formal limit def of the derivative to fond the derivative of f(x)=(sqrt 2x)-5 at x=2

Answer 1

f'(2) = lim h->0 { f(2+h) - f(2) } / h

Answer 2

I'm having trouble distributing the radicals

Answer 3

\[(\frac{ \sqrt{2(x+h)} -5 - (\sqrt{2x}-5) }{ h}) (\frac{ \sqrt{2x +5} }{ \sqrt{2x +5} })\]

Answer 4

They want the derivative evaluated at x = 2. It would be less complicated if you put x = 2 as indicated in my first reply.

Answer 5

\[\sqrt{4+2h}-2 ??\]

Answer 6

f(2+h) = sqrt(2(2+h)) - 5
f(2) = sqrt(4) - 5
subtract:
sqrt(4+2h) - 2

lim h->0 { sqrt(4+2h) - 2 } / h

Multiply top and bottom by { sqrt(4+2h) + 2 }

Answer 7

Use; (a+b)(a-b) = a^2 - b^2 when multiplying the numerator.

Answer 8

is it just \[\sqrt{4+2h}\]

Answer 9

\[\frac{\sqrt{2x+h}-2}{h}\]

Answer 10

\[\lim_{h \rightarrow 0} \frac{ \sqrt{4+2h} - 2 }{ h } * \frac{ \sqrt{4+2h} + 2 }{\sqrt{4+2h} + 2 } = \frac{4+2h-4}{h(\sqrt{4+2h} +2)}\]

Answer 11

lim h->0 2 / { sqrt(4 + 2h) + 2 } = 2 / (2+2) = 1/2

Answer 12

ooooh okay now i see….. thank you for expelling it so well!

Answer 13

You are welcome.