Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify).
C) 5
D) The limit does not exist.

Question

Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify). 
C) 5 
D) The limit does not exist.

Quizplus · Accepted Answer

We can use the conjugate expression to simplify the limit as follows:

lim x→2 [(x-2)/(x^2-4)]^(1/3)

= lim x→2 [(x-2)/(x-2)(x+2)]^(1/3)

= lim x→2 [(1)/(x+2)]^(1/3)

Now, we can substitute 2 into the expression to get:

[(1)/(2+2)]^(1/3) = (1/4)^(1/3) = 1/∛4

So, the limit is 1/∛4, which is approximately 0.629.

Therefore, the best choice is B.

Find the Limit Exactly (Hint: Multiply and Divide by the Conjugate