Question

`f(x) = √(x)`
Lim h=0
f(x+h) -f(x)/h​

Answer 1

Answer:
`(1)/(2\sqrt x)`

Explanation:

`\lim_(h \to 0) f(x)=(f(x+h)-f(x))/(h)`

f(x) =
`\sqrt x\\`

f(x+h) =
`√(x+h)`

`\lim_(h \to 0) f(x)=(√(x+h)-\sqrt x)/(h)`

`=(√(x+h)-\sqrt x)/(h)\bigg((√(x+h)+\sqrt x)/(√(x+h)+\sqrt x)\bigg)`

`=((x + h)-(x))/(h(√(x+h)+\sqrt x))`

`=(h)/(h(√(x+h)+\sqrt x))`

`=(1)/(√(x+h)+\sqrt x)`

`=(1)/(√(x+0)+\sqrt x)`

`=(1)/(2\sqrt x)`