Download App

Limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow\infty}\Big(\text{a}^{\frac{1}{\text{x}}}-1\Big)\text{x}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow\infty}\Big(\text{a}^{\frac{1}{\text{x}}}-1\Big)\text{x}$
Let $ \frac{1}{\text{x}}=\text{h}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{\big(\text{a}^\text{h}-1\big)}{\text{h}}$
$=\text{log a}$

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 "2 Marks Questions" from Limits→Limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

In a single throw of a die describe the following events:
F = Getting a number not less than 3.
Also, find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and F.
→
If $(n + 1)! = 90 [(n - 1)!],$ find $n.$
→
Let $\text{f(x)}=\begin{cases}\text{x}+1, & \text{if x}> 0\\\text{x}-1, &\text{if x} < 0\end{cases}.$ Prove that $\lim\limits_{\text{x}\rightarrow0}\text{f(x)}$ does not exist.
→
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
→
Evaluate the following:
$\text{i}^{37}+\frac{1}{\text{i}^{67}}$
→
Find the equation of hyperbola having Foci $(0, \pm 13)$ and the conjugate axis is of length $24.$
→
Insert $5$ geometric means between $\frac{32}{9}$ and $\frac{81}{2}.$
→
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
→
Differentiate the following function with respect to $(\text{x})$:$\frac{\text{a}\cos\text{x}+\text{b}\sin\text{x}+\text{c}}{\sin\text{x}}$
→
There are $10$ persons named $P_1, P_2, P_3, ...., P_{10}.$ Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement $P_1$  must occur whereas $P_4$ and $P_5$ do not occur. Find the number of such possible arrangements.
→