Q87 / 200 · AP EAMCET 2001 · Mathematics

$\lim _{x \rightarrow-}\left(\frac{x+a}{x+b}\right)^{a+b}$ is equal to

  • Correct answer
    A
    $1$
  • B
    $e^{b-a}$
  • C
    $e^{a-b}$
  • D
    $e^b$

Solution

$\lim _{x \rightarrow \infty}\left(\frac{x+a}{x+b}\right)^{a+b}=\lim _{x \rightarrow \infty}\left(\frac{1+\frac{a}{x}}{1+\frac{b}{x}}\right)^{a+b}=(1)^{a+b}=1$

Hence, the correct answer is option: 'A'.

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