Question

If lim ₓ₋ₐ (x⁴ - 1)/(x - 1) = limₓ₋ₖ (x³ - k³)/(x² - k²),
then k is
(A) 3/8
(B) 8/3
(C) 4/3
(D) 3/2

Answer 1

Given,

lim ₓ₋ₐ (x⁴ - 1)/(x - 1) = limₓ₋ₖ (x³ - k³)/(x² - k²)

•Let us first solve the left hand side of the equation.

•we get the value as

lim ₓ₋ₐ (x⁴ - 1)/(x - 1) = 4.

•Now, Solving the right hand side we get

limₓ₋ₖ (x³ - k³)/(x² - k²) = 3k/2

• Now , equating both sides we get k=8/3.

•Hence, Option B is the right answer.