Q100 / 160 · AP EAMCET 2022 (07 Jul Shift 2) · Mathematics

$\lim _{x \rightarrow-a} \frac{x^7+a^7}{x+a}=7 \Rightarrow a=$

  • A
    $\pm 7$
  • B
    $\pm 6$
  • Correct answer
    C
    $\pm 1$
  • D
    $\pm 2$

Solution

$\begin{aligned} & =\lim _{x \rightarrow-a} \frac{x^7+a^7}{x+a}=7 \\ & \Rightarrow \quad 7(-a)^6=7 \\ & \Rightarrow \quad(-a)^6=1 \\ & \Rightarrow \quad-a= \pm 1 \\ & \Rightarrow \quad a= \pm 1 \\ & \end{aligned}$

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

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