For the real parameter

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

For the real parameter aa, consider the limit L(a)=lim⁡x→∞2x2a+5x3a−7\displaystyle L(a)=\lim_{x\to\infty}\dfrac{2x^{2a}+5}{x^{3a}-7}. For which of the following sets of aa does L(a)L(a) exist and equal 00? (a) All real a<0a<0 (b) a=0a=0 only (c) No real values of aa (d) All real a>0a>0

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