Evaluate the following limit: _ x 0 e^ 3x -e^ 2x x - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{3\text{x}}-\text{e}^{2\text{x}}}{\text{x}}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{3\text{x}}-\text{e}^{2\text{x}}}{\text{x}}$ $=3\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{3\text{x}}-1\text{}}{3\text{x}}-\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^{2\text{x}}-1\text{}}{2\text{x}}$ $=3-2$ $=1$

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

Write the contrapositive and converse of the following statements. You cannot comprehend geometry if you do not know how to reason deductively.

Evaluate $\mathop {\lim }\limits_{x \to 0} \frac{{\cos x}}{{\pi - x}}$

For any two sets A and B, show that the following statements are equevalent: $\text{A}\cup\text{B}=\text{B}.$

Find the locus of a point equidistant from the point(2, 4) and the y-axis.

The line through the points (h, 3) and (4, 1) intersects the line 7x - 9y - 19 = 0 at right angle. Find the value of h.

Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of a square.

For the relation R₁ defined on R by the rule $(\text{a, b})\in\text{R}_1\Leftrightarrow1+\text{ab}>0$
Prove that, $(\text{a, b})\in\text{R}_1$ and $(\text{a},\text{b})\in\text{R}_1$ and $(\text{b},\text{c})\in\text{R}_1\Rightarrow(\text{a, c})\in\text{R}_1$ is not true for all $\text{a, b, c}\in\text{R}$

Express $(5-3 i)^3$ in the form $a+i b$.

Solve – 8 $\le$ 5x – 3 < 7.

Find the equation of ellipse having Foci ($\pm$3, 0), a = 4.