Download App

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

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to \infty } [x({a^{1/x}} - 1)]$,$(a > 1) = $
  • A
    $\log x$
  • B
    $1$
  • C
    $0$
  • ✓
    $ - \log \frac{1}{a}$
✓

Answer

Correct option: D.
$ - \log \frac{1}{a}$
d
(d) $\mathop {\lim }\limits_{x \to \infty } x\,({a^{1/x}} - 1) = \mathop {\lim }\limits_{x \to \infty } \,\left[ {\frac{{{a^{1/x}} - 1}}{{1/x}}} \right]$

$ = \mathop {\lim }\limits_{x \to \infty } \frac{{[{e^{{{\log }_e}{a^{1/x}}}} - 1]}}{{1/x}} = {\log _e}a = - {\log _e}\frac{1}{a}.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 11 - 12. limits→STD 11 - 12. limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively such that $m \le n.\,$ A mapping is selected at random from the set of all mappings from $A$ to $B$. The probability that the mapping selected is an injection is
→
The coordinates of a point which is in YZ - plane are :
→
If $\sum\limits_{r = 0}^{25} {\left\{ {^{50}{C_r}.{\,^{50 - r}}{C_{25 - r}}} \right\} = K\left( {^{50}{C_{25}}} \right)} $, then $K$ is equal to
→
The equations of the normals to the circle ${x^2} + {y^2} - 8x - 2y + 12 = 0$ at the points whose ordinate is $-1,$ will be
→
The domain of the function $\text{f(x)}=\sqrt{2-2\text{x}-\text{x}^2}$ is:
→
If three distinct number $a, b, c$ are in $G.P.$ and the equations $ax^2 + 2bc + c = 0$ and $dx^2 + 2ex + f = 0$ have a common root, then which one of the following statements is correct?
→
Let $E$ denote the set of all integers a such that the point of intersection of the parabola $y = x ^2+2 ax +2021$ with $x$-axis has rational coordinates. The largest element of $E$ is
→
The number of ordered pairs ( $\mathrm{r}, \mathrm{k}$ ) for which $6 \cdot ^{35} \mathrm{C}_{\mathrm{r}}=\left(\mathrm{k}^{2}-3\right)\cdot{^{36} \mathrm{C}_{\mathrm{r}+1}}$. where $\mathrm{k}$ is an integer, is
→
The equation of the tangent to the parabola ${y^2} = 4ax$ at point $(a/{t^2},\;2a/t)$ is
→
If $2 \sin ^3 x+\sin 2 x \cos x+4 \sin x-4=0$ has exactly $3$ solutions in the interval $\left[0, \frac{\mathrm{n} \pi}{2}\right], \mathrm{n} \in \mathrm{N}$, then the roots of the equation $x^2+n x+(n-3)=0$ belong to :
→