Mathematics

Problem

Evaluate the limits given below. Show all the intermediate steps clearly. a. (i)

\displaystyle \lim_{x\to -\infty} x^{4}e^{2x}

b. (ii)

\displaystyle \lim_{x\to \infty} x^{4}e^{-2x}

c. (iii) Are the two limits obtained in parts (i) and (ii) equal? Give a brief reason for your answer.