Differentiation Question 37
Question: $ \underset{x\to \infty }{\mathop{\lim }}{{( \frac{x^{2}+5x+3}{x^{2}+x+3} )}^{1/x}} $ is equal to
Options:
A) $ e^{4} $
B) $ e^{2} $
C) $ e^{3} $
D) 1
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ \underset{x\to \infty }{\mathop{\lim }}-{{( \frac{x^{2}+5x+3}{x^{2}+x+3} )}^{1/x}}=\underset{x\to \infty }{\mathop{\lim }}{{( \frac{1+\frac{5}{x}+\frac{3}{x^{2}}}{1+\frac{1}{x}+\frac{3}{x^{3}}} )}^{1/x}}=1^{o}=1 $
BETA
