Download App

Limits — MATHS STD 11 Science — Question

Gujarat 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 "(Each question 2 marks)" from Limits→Limits — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Given two mutually exclusive events A and B such that $\text{P(A)} = \frac{1}{2}$ and $\text{P(B)} = \frac{1}{3},$ find P(A or B).
→
Express the $(-5i)\left(\frac 18 i\right)$ in the form of a+bi.
→
Find the principal solution of the equation: sin x = $\frac { \sqrt { 3 } } { 2 }$
→
In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?
→
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
→
Find the general solutions of the following equations:$\sin\text{x}=\frac{1}{2}$
→
A point R with x-coordinate 4 lies on the line segment joining the points P(2, -3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint Suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by $\left(\frac{8 k+2}{k+1}, \frac{-3}{k+1}, \frac{10 k+4}{k+1}\right)$].
→
Express $(-\sqrt3 + \sqrt{-2})(2\sqrt3 - i)$ in the form of a + ib.
→
Show that the set of letters needed to spell CATARACT and the set of letters needed to spell TRACT are equal.
→
Evaluate the following one sided limits: $\lim\limits_{\text{x}\rightarrow\frac{-\pi}{2^+}}\sec\text{x}$
→