lim_x→ 2x^5 32x^2 4 =lim_x→21x+2x^5 2^5x 2 =lim_x→ 21x+2lim_x→2x^5 2^5x 2 =12+25×2^5 1=14×5×2^4 =20 ...

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Theorems on Integration

if limx→ 2 ...

Question

if $lim x \to 2 \frac{x^{5} - 32}{x^{2} - 4}$

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Solution

$l i m_{x \to 2} \frac{x^{5} - 32}{x^{2} - 4} = l i m_{x \to 2} \frac{1}{x + 2} \frac{x^{5} - 2^{5}}{x - 2} = {lim}_{x \to 2} \frac{1}{x + 2} l i m_{x \to 2} \frac{x^{5} - 2^{5}}{x - 2} = \frac{1}{2 + 2} 5 \times 2^{5 - 1} = \frac{1}{4} \times 5 \times 2^{4} = 20$

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