The limit of the indeterminate quotient lim (x-->4) [2-(x^1/2)]/[3-(2x+1)^1/2] evaluates to 3/4. The solution involves rationalizing both the numerator and denominator, followed by factoring out (4-x) from both. Careful attention to parentheses is crucial during the simplification process to avoid errors in calculation.
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p.ella said: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 said:Next factor 4-x out of the numerator and denominator. And be careful. You are missing some parentheses there.