Finding the Limit of f(x)=(x+1)^(1/2)

[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

Homework Equations

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

 

[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?

 

[Mark44]

Homework Statement

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

Homework Equations

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