Evaluate the following limit: _ x 0 e^ x -e ^ x- - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{ x }-\text{e }^{\sin\text{x}}}{\text{x}-\sin\text{x}}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{ x }-\text{e }^{\sin\text{x}}}{\text{x}-\sin\text{x}}$ $=\lim\limits_{\text{x}\rightarrow0 }\text{e}^{ \sin \text{x}}\Big[\frac{\text{e}^{\text{ x }-\sin\text{x}}-1}{\text{x}-\sin\text{x}}\Big]$ $=1\times\text{log e}$ $=1$

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 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: $\text{A}\cap(\text{B}\cup\text{C})$

Find the equation of a line for which: $\text{p}=4,\alpha=150^\circ$

Find the equation of ellipse which has vertices ($\pm$ 5, 0), foci ($\pm$4, 0)

A bag contains one white and one red ball. A ball is drawn from the bag. If the ball drawn is white it is replaced in the bag and again a ball is drawn. Otherwise, a die is tossed. Write the sample space for this experiment.

Find the derivative of $(x^3 - 27)$ from first principle.

Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?

Represent the complex number z = 1 + $i \sqrt { 3 }$ in the polar form.

Find the derivative of f(x) = 3x at x = 2

Find the locus of a point which is equidistant from (1, 3) and the x-axis.

Show the following quadratic equation: $x^2 - (2 + i) x - (1 - 7i) = 0$