lim_x→ 2x^5 ( 2)^5x 2x^3 ( 2)^3x 2 =5( 2)^5 13( 2)^3 1 since lim_x→ ax^n a^nx a=na^n 1 =5( 2)^43( 2)^2 =5× 163× 4 =203 ...

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Continuity of a Function

limx → -2x5+3...

Question

$lim x \to - 2 \frac{x^{5} + 32}{x^{3} + 8}$

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Solution

${lim}_{x \to - 2} \frac{\frac{x^{5} - {(- 2)}^{5}}{x - 2}}{\frac{x^{3} - {(- 2)}^{3}}{x - 2}}$
$= \frac{5 {(- 2)}^{5 - 1}}{3 {(- 2)}^{3 - 1}}$ since ${lim}_{x \to a} \frac{x^{n} - a^{n}}{x - a} = n a^{n - 1}$
$= \frac{5 {(- 2)}^{4}}{3 {(- 2)}^{2}}$
$= \frac{5 \times 16}{3 \times 4}$
$= \frac{20}{3}$

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