Limit of Radical Quotients: Is the Answer 3/4?

[p.ella]

Homework Statement

Evaluate the limit of each indeterminate quotient:

lim (x-->4) [2-(x^1/2)]/[3-(2x+1)^1/2]

Homework Equations

The Attempt at a Solution

The answer in the book is 3/4. This MAY be wrong though.

My attempt: I basically tried rationalizing the numerator AND denominator but got stuck here:

lim (x-->4) [12-3x+(4-x(2x+1)^1/2) ] / [16-4x+(8-2x(x)^1/2)]

 

[Dick]

Homework Statement

Evaluate the limit of each indeterminate quotient:

lim (x-->4) [2-(x^1/2)]/[3-(2x+1)^1/2]

Homework Equations

The Attempt at a Solution

The answer in the book is 3/4. This MAY be wrong though.

My attempt: I basically tried rationalizing the numerator AND denominator but got stuck here:

lim (x-->4) [12-3x+(4-x(2x+1)^1/2) ] / [16-4x+(8-2x(x)^1/2)]

Next factor 4-x out of the numerator and denominator. And be careful. You are missing some parentheses there.

 

[p.ella]

Next factor 4-x out of the numerator and denominator. And be careful. You are missing some parentheses there.

Thank you! :)