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STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
MCQ
$\mathop {\lim }\limits_{x \to \infty } \frac{{\log {x^n} - [x]}}{{[x]}},\,n \in N,\,$$\,(\,[x]$ denotes greatest integer less than or equal to $x$)
  • ✓
    Has value $-1$
  • B
    Has value $0$
  • C
    Has value $1$
  • D
    Does not exist
✓

Answer

Correct option: A.
Has value $-1$
a
(a)$\mathop {\lim }\limits_{x \to \infty } \frac{{\log {x^n} - [x]}}{{[x]}} = \mathop {\lim }\limits_{x \to \infty } \frac{{\log {x^n}}}{{[x]}} - \mathop {\lim }\limits_{x \to \infty } \frac{{[x]}}{{[x]}}$$ = 0 - 1 = - 1.$

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