SOLUTION: Kindly help me solving it I tried my best but I couldn't lim (1-x^(-1/3))/1-x^(-2/3) is equal to x-->1 A)-1/2 B)1/2 C)2 D)none of these

Algebra ->  Functions -> SOLUTION: Kindly help me solving it I tried my best but I couldn't lim (1-x^(-1/3))/1-x^(-2/3) is equal to x-->1 A)-1/2 B)1/2 C)2 D)none of these      Log On


   



Question 1044671: Kindly help me solving it I tried my best but I couldn't
lim (1-x^(-1/3))/1-x^(-2/3) is equal to
x-->1
A)-1/2
B)1/2
C)2
D)none of these

Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.
Kindly help me solving it I tried my best but I couldn't
lim (1-x^(-1/3))/1-x^(-2/3) is equal to
x-->1
A)-1/2
B)1/2
C)2
D)none of these
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First, you incorrectly wrote your formula.
Why did you use the parentheses for the numerator and didn't use it for the denominator?


Second, ask yourself what happens with x^(-1/3) when x-->1 ?


Third, introduce the new variable y = x^(-1/3) and rewrite the formula in terms of this new variable.


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's factor and simplify











Difference of Squares rule



Notice how the terms cancel



Now use substitution to plug in x = 1














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So,




which means the final answer is choice B) 1/2