(a) Show that for any non-zero real constant , the limit _ x 4x^ 3 +7x^ 2 -5 kx^ 3…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

(a) Show that for any non-zero real constant

k

, the limit

\lim_{x\to\infty}\frac{4x^{3}+7x^{2}-5}{kx^{3}-2x+1}

exists and equals

\dfrac{4}{k}

. (b) Hence determine the value of

k

for which the limit is exactly

2