mathop {lim }limits_{x to infty } frac{{log { | vedclass

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(A) આપણને લક્ષ $\mathop {\lim }\limits_{x 	o \infty } \frac{{\log {x^n} - [x]}}{{[x]}}$ આપેલ છે.આને $\mathop {\lim }\limits_{x 	o \infty } \left( \f

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કિંમત $-1$ છે

Vedclass · Answer

(A) આપણને લક્ષ $\mathop {\lim }\limits_{x 	o \infty } \frac{{\log {x^n} - [x]}}{{[x]}}$ આપેલ છે.આને $\mathop {\lim }\limits_{x 	o \infty } \left( \frac{{\log {x^n}}}{{[x]}} - \frac{{[x]}}{{[x]}} ight)$ તરીકે લખી શકાય.જેમ $x 	o \infty,$ $[x] \approx x$ થાય.તેથી,$\mathop {\lim }\limits_{x 	o \infty } \frac{{\log {x^n}}}{{[x]}} = \mathop {\lim }\limits_{x 	o \infty } \frac{{n \log x}}{x} = 0.$આમ,અંતિમ જવાબ $0 - 1 = -1$ મળે છે.

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