Evaluate the following limit: _ x 0 a^x+b^x-2 x - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{x}+\text{b}^\text{x}-2}{\text{x}}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{x}+\text{b}^\text{x}-2}{\text{x}}$ $=\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{x}-1}{\text{x}}+\lim\limits_{\text{x}\rightarrow0}\frac{\text{b}^\text{x}-1}{\text{x}}$ $=\text{loga}+\text{logb}$ $=\text{log (ab)}$

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

Solve $- x^2 + x - 2 = 0$

Which trem of the A.P. 3, 8, 13, ...os 248?

If E and F are events such that P(E) = $\frac{1}{4}$, P(F) = $\frac{1}{2}$ and P(E and F) = $\frac{1}{8}$. Find
(i) P (E or F) (ii) P (not E and not F)

How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?

Find: 10th term of the A.P. 1, 4, 7, 10, ...

Prove that: $\sin50^\circ+\sin10^\circ=\cos20^\circ$

The points A(2, 0), B(9, 1), C(11, 6)and D(4, 4) ar the vertices of a quadrilateral ABCD, Determine whether ABCD is a rhombus or not.

Prove that: $\begin{equation} \frac{\sin (x+y)}{\sin (x-y)}=\frac{\tan x+\tan y}{\tan x-\tan y} \end{equation}$

Given that P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear. Find the ratio in which Q divides PR.

Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.