Question

If $\underset{x\to -a}{lim}\frac{x^7+a^7}{x+a}=7$, then the value of $a$ is=? (where a is a real number)

• A. $1$
• B. $-1$
• C. $7$
• D. $-7$

Answer 1

Answer: (A), (B)

The correct options are
A $1$
B $-1$

Given, $\underset{x⟶-a}{lim}\frac{x^7+a^7}{x+a}=7$

$\Rightarrow \underset{x⟶-a}{lim}\frac{x^7-({-a)}^7}{x^1-{(-a)}^1}=7$

$\Rightarrow \frac{7}{1}{(-a)}^{7-1}=7$ ....$(\because \underset{x⟶a}{lim}\frac{x^m-a^m}{x^n-a^n}=\frac{m}{n}{a}^{m-n})$

$\Rightarrow {(-a)}^6=1$

$\Rightarrow a=\pm 1$ .....We take the real roots only