Evaluate lim x - 1x15-1-x0-1

X → 1lim x^15 1/x^10 1 x → 1lim x^15 1/x^10 1=x → 1lim{(x^15 1/x 1 ) +(x^10 1/x 1 )} =x → 1lim(x^15 1/x 1+ ) x → 1lim(x^10 1/x 1 ) =(15×1^14)+(10× 1^9)=15/10= ...

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Byju's Answer

Standard XII

Mathematics

Sandwich Theorem

Evaluate lim ...

Question

Evaluate $l i m x \to 1 \frac{x^{15} - 1}{x^{10} - 1}$

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Solution

$l i m x \to 1 \frac{x^{15} - 1}{x^{1} 0 - 1}$

$l i m x \to 1 \frac{x^{15} - 1}{x^{10} - 1} = l i m x \to 1 {(\frac{x^{15} - 1}{x - 1}) + (\frac{x^{10} - 1}{x - 1})}$

$= l i m x \to 1 (\frac{x^{15} - 1}{x - 1} +) l i m x \to 1 (\frac{x^{10} - 1}{x - 1})$

$= (15 \times 1^{14}) + (10 \times 1^{9}) = \frac{15}{10} = \frac{3}{2}$

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Similar questions

Q. Evaluate :

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lim x \to 1 \frac{x^{15} - 1}{x^{10} - 1}

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

Q. Assertion :

lim x \to 1 \frac{x^{15} - 1}{x^{10} - 1} = \frac{3}{2}

Reason:

lim x \to a \frac{x^{n} - a^{n}}{x - a} = n a^{n - 1}

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lim x \to 1 \frac{x^{15} - 1}{x^{10} - 1}

Q. Evaluate:

lim x \to 0 \frac{2^{x} - 1}{\sqrt{x + 1} - 1}

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Evaluate limx→1x15−1x10−1

limx→1 x15−1x10−1 limx→1 x15−1x10−1=limx→1{(x15−1x−1)+(x10−1x−1)} =limx→1(x15−1x−1+)limx→1(x10−1x−1) =(15×114)+(10×19)=1510=32

Evaluate $l i m x \to 1 \frac{x^{15} - 1}{x^{10} - 1}$