Evaluate the following limit: _ x 0 a^mx-1 b^nx-1 ,n =0 - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{mx}-1}{\text{b}^\text{nx}-1},\text{n}\not=0$

✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{mx}-1}{\text{b}^\text{nx}-1},\text{n}\not=0$ $=\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{mx}-1}{\text{mx}}\times\frac{1}{\lim\limits_{\text{x}\rightarrow0}\frac{\text{b}^\text{nx}-1}{\text{nx}}}\times\frac{\text{m}}{\text{n}}$ $=\frac{\text{mloga}}{\text{nlogb}},\text{n}\not=0$

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

If $\cos\text{x}=\frac{4}{5}$ and x is acute, find $\tan 2\text{x}$

Solve – 8 $\le$ 5x – 3 < 7.

Prove that: $\frac { \cos 4 x + \cos 3 x + \cos 2 x } { \sin 4 x + \sin 3 x + \sin 2 x }$= cot 3x.

Prove that: $\frac{1-\cos2\text{x}+\sin2\text{x}}{1+\cos2\text{x}+\sin2\text{x}}=\tan\text{x}$

Find the general solutions of the following equations: $\sin2\text{x}=\frac{\sqrt{3}}{2}$

Prove that: $\cos^2\frac{\pi}{8}+\cos^2\frac{3\pi}{8}+\cos^2\frac{5\pi}{8}+\cos^2\frac{7\pi}{8}=2$

Find the coordinates of the foci, and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. $9y^2 - 4x^2 = 36$

Find what the following equations become when the origin is shifted to the point $(1,1) ? x^2+y^2-2 x-2 y=0$

Draw the lines x = -3, x = 2, y = -2, y = 3 and write the coordinates of the vertices of the square so formed.

Solve the following system of equations in R. $11-5\text{x}>-4, \ 4\text{x}+13\leq-11$