Download App

Limits — MATHS STD 11 Science — Question

Rajasthan 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→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the sum of the following geometric progrssions:

1, 3, 9, 27, ... to 8 terms

→
If $C _0, C _1, C _2, \ldots \ldots . C _n$ are the binomial coefficients in the expansion of $(1+x)^n$, then prove that :
$C_0-\frac{C_1}{2}+\frac{C_2}{3}-\frac{C_3}{4}+\ldots \ldots \ldots+\frac{(-1)^n \cdot C_n}{n+1}=\frac{1}{n+1}$
→
Two dice are thrown. The events A, B, C, D, E and F are described as follows:
A = Getting an even number on the first die.
B = Getting an odd number on the first die.
C = Getting at most 5 as sum of the numbers on the two dice.
D = Getting the sum of the numbers on the dice greater than 5 but less than 10.
E = Getting at least 10 as the sum of the numbers on the dice.
F = Getting an odd number on one of the dice.
Describe the following events:
A and B, B or C, B and C, A and E, A or F, A and F.
→
Find the value of the following trigonomentric ratio:
$\cos\Big(\frac{39\pi}{4}\Big)$
→
Prove that:
$
\sin ^2 \frac{\pi}{18}+\sin ^2 \frac{\pi}{9}+\sin ^2 \frac{7 \pi}{18}+\sin ^2 \frac{4 \pi}{9}=2
$
→
Find the equation of ellipse which has Vertices ($\pm$6, 0), foci ($\pm$4, 0)
→
Prove that: cos 4x = 1 - 8sin2x cos2x
→
Find the modulus and argument of the following complex numbers and hence express each of them in the polar form:
$1+\text{i}$
→
Check whether the probabilities $P ( A )$ and $P ( B )$ are consistently defined $P ( A )=0.5, P ( B )=0.4, P(A \cup B)=0.8$
→
If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11}, and D = {10, 11, 12, 13, 14}. Find:
$\text{A}\cap(\text{B}\cup\text{C})$
→