Limit Problem

Prototype44

Homework Statement

lim f(x+h)-f(x)/h f(x)=(x+1)^(1/2) ans:1/2(x+1)^(1/2)
h→0

The Attempt at a Solution

lim (x+h+1)^(1/2)-(x+1)^(1/2)/h lim (x+1)^(1/2)-(x+1)^(1/2)/h
h→0 h→0

Should the answer be D.N.E because the square roots cancel each other and leave 0/0

Last edited:

SithsNGiggles
$\lim_{h \to 0} \frac{\sqrt{x+h+1}-\sqrt{x+1}}{h}$

Have you tried multiplying the numerator and denominator by the conjugate of the numerator?

Mentor

Homework Statement

lim f(x+h)-f(x)/h f(x)=(x+1)^(1/2) ans:1/2(x+1)^(1/2)
h→0

The Attempt at a Solution

lim (x+h+1)^(1/2)-(x+1)^(1/2)/h lim (x+1)^(1/2)-(x+1)^(1/2)/h
h→0 h→0

Should the answer be D.N.E because the square roots cancel each other and leave 0/0
No. This type of limit always is of the [0/0] indeterminate form.

Prototype44
Figured it out