Limx #8594;1 #160;x15 1x10 1=limx #8594;1 #160;x15 115x 1 #215;x 1x10 110=15115 110110 1=32 ...

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Value of an Expression

lim x → 1 x15...

Question

$\lim_{x \to 1} \frac{x^{15} - 1}{x^{10} - 1}$

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Solution

$\lim_{x \to 1} [\frac{x^{15} - 1}{x^{10} - 1}] = \lim_{x \to 1} [\frac{x^{15} - {(1)}^{15}}{x - 1} \times \frac{x - 1}{x^{10} - {(1)}^{10}}] = \frac{15 {(1)}^{15 - 1}}{10 {(1)}^{10 - 1}} = \frac{3}{2}$

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