If [ _x 1 x^4 - 1 x - 1 = _x k x^3 - k^3 x^2 - k^2], then k is :

Question

If $$\mathop {\lim }\limits_{x \to 1} {{{x^4} - 1} \over {x - 1}} = \mathop {\lim }\limits_{x \to k} {{{x^3} - {k^3}} \over {{x^2} - {k^2}}}$$,  then k is :

Accepted Answer

If $$\mathop {\lim }\limits_{x \to 1} {{{x^4} - 1} \over {x - 1}} = \mathop {\lim }\limits_{x \to K} \left( {{{{x^3} - {k^3}} \over {{x^2} - {k^2}}}} \right)$$

L\cdot H\cdot S\cdot

$$\mathop {Lt}\limits_{x \to 1} {{{x^4} - 1} \over {x - 1}} = \left( {{0 \over 0}form} \right)$$

$$ \Rightarrow \mathop {Lt}\limits_{x \to 1} {{4{x^3}} \over 1} = 4$$

Now, $$\mathop {\lim }\limits_{x \to K} \left( {{{{x^3} - {k^3}} \over {{x^2} - {k^2}}}} \right)$$ = 4

$$ \Rightarrow \mathop {\lim }\limits_{x \to K} {{3{x^2}} \over {2x}} = 4$$

$$ \Rightarrow {3 \over 2}k = 4 \Rightarrow k = {8 \over 3}$$

Solutions · 1