If l i m x → 1 x 4 - 1 x - 1 = l i m x → k x 3 - k 3 x 2 - k 2 , then k is

Open MARKS Web Download App

Search any question & find its solution

Question: Answered & Verified by Expert

If

\underset{x \to 1}{l i m} \frac{x^{4} - 1}{x - 1} = \underset{x \to k}{l i m} \frac{x^{3} - k^{3}}{x^{2} - k^{2}}

, then

k

is

MathematicsLimitsJEE MainJEE Main 2019 (10 Apr Shift 1)

Options:

A $\frac{3}{2}$
B $\frac{4}{3}$
C $\frac{3}{8}$
D $\frac{8}{3}$

Solution:

2514 Upvotes Verified Answer

The correct answer is:

\frac{8}{3}

Given limits can be written as,

$\underset{x \to 1}{l i m} \frac{(x^{2} + 1) (x + 1) (x - 1)}{(x - 1)} = \underset{x \to k}{l i m} \frac{(x - k) (x^{2} + k^{2} + x k)}{(x - k) (x + k)}$
$\Rightarrow 4 = \frac{3 k^{2}}{2 k}$
$\Rightarrow k = \frac{8}{3}$ .

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play