Let be a real number

MATHEMATICS · Subjective · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

Let

k

be a real number. Evaluate

L(k)=\lim_{x\to\infty}\frac{3x^{4}-x^{3}+6}{(k-1)x^{5}+2kx^{4}-7}

whenever the limit is finite. Hence find (i) the set of all real values of

k

for which

L(k)=0

, (ii) the set of all real values of

k

for which

L(k)

is a non-zero finite constant, (iii) the set of all real values of

k

for which the limit does not exist as a finite real number.