The value of lim x -x-110-x-210-x-10010-x10-1010 is

The correct option is A 100 lim_x →∞(x + 1)^10+ (x +2)^10+ ⋯ + (x + 100)^10/x^10 +10^10 Dividing N' and D' by x^10 = lim_x →∞(1 + 1/x )^10 + (1 + 2/x )^10+ ⋯ ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

The value of ...

Question

The value of ${lim}_{x \to \infty} \frac{(x + 1)^{10} + (x + 2)^{10} + \dots + (x + 100)^{10}}{x^{10} + 10^{10}}$ is

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100

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$10^{10}$

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None of these

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Solution

The correct option is B
100

${lim}_{x \to \infty} \frac{(x + 1)^{10} + (x + 2)^{10} + \dots + (x + 100)^{10}}{x^{10} + 10^{10}}$
Dividing N' and D' by $x^{10}$
$= {lim}_{x \to \infty} \frac{{(1 + \frac{1}{x})}^{10} + {(1 + \frac{2}{x})}^{10} + \dots + {(1 + \frac{100}{x})}^{10}}{1 + \frac{10^{10}}{x^{10}}}$
$= 1 + 1 + 1 + \dots + 100 t i m e s$
$= 100$

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Similar questions

lim x \to \infty \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . . {(x + 100)}^{10}}{x^{10} + 10^{10}}

lim x \to \infty \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . . + {(x + 100)}^{10}}{x^{10} + 10^{10}}

Q. Evaluate:

lim x \to \infty \frac{(x + 1)^{10} + (x + 2)^{10} + \dots . . + (x + 100)^{10}}{x^{10} + 10^{10}}

Q. The value of

\lim_{x \to \infty} \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . + {(x + 100)}^{10}}{x^{10} + 10^{10}}

is

(a) 10

(b) 100

(c) 10¹⁰

(d) none of these

Q. Assertion :

lim x \to \infty \frac{(x + 1)^{10} + (x + 2)^{10} + . . . + (x + 100)^{10}}{x^{10} + 9^{10}} = 100

p (x)

and q(x) are polynomials of same degree, then Reason:

lim x \to \infty \frac{p (x)}{q (x)} = \frac{l e a d i n g c o e f f i c i e n t s o f p (x)}{l e a d i n g c o e f f i c i e n t s o f q (x)}

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The value of limx→∞(x+1)10+(x+2)10+⋯+(x+100)10x10+1010 is

The correct option is B 100 limx→∞(x+1)10+(x+2)10+⋯+(x+100)10x10+1010 Dividing N' and D' by x10 =limx→∞(1+1x)10+(1+2x)10+⋯+(1+100x)101+1010x10 =1+1+1+⋯+100times =100

The value of ${lim}_{x \to \infty} \frac{(x + 1)^{10} + (x + 2)^{10} + \dots + (x + 100)^{10}}{x^{10} + 10^{10}}$ is