Evaluate _ x 0 e^ k x -1 x . - Vidyadip

Question

Evaluate $\lim _{x \rightarrow 0} \frac{e^{k x}-1}{x}$.

✓

Answer

We have, $\lim _{x \rightarrow 0} \frac{e^{b x}-1}{x}=\lim _{x \rightarrow 0} \frac{e^{b_x}-1}{x} \times \frac{b}{b}$
[multiplying numerator and denominator by b]
$=\lim _{x \rightarrow 0} \frac{b\left(e^{b x}-1\right)}{b x}$
On putting $h = bx$ and as $x \rightarrow 0$, then $h \rightarrow 0$, we get
$\begin{array}{l}\lim _{x \rightarrow 0} \frac{e^x-1}{x}=b \lim _{h \rightarrow 0} \frac{\left(e^h-1\right)}{h} \\ =b \times 1\left[\because \lim _{x \rightarrow 0} \frac{e^x-1}{x}=1\right] \\ = b \end{array}$

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 "2 Marks Questions" from Model Paper 9→Model Paper 9 — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the coordinates of the points which tisect the line segment joining the points P(4, 2, -6) and Q(10, -16, 6).

The runs scored by players in $10$ matches are $38, 70, 48, 34, 42, 55, 63, 46, 54, 44.$ Find the variance and standard deviation.

If the straight line through the point P (3, 4) makes an angle $\frac{\pi}{6}$ with the x-axis and meets the line 12x + 5y + 10 = 0 at Q, find the length PQ.

Find the equation of hyperbola having Foci ($\pm$4, 0) and the latus rectum is of length 12.

Find the domain of the function f(x) = $\begin{equation} \frac{x^{2}+3 x+5}{x^{2}-5 x+4} \end{equation}$

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

Find the domain and range of the function $f(x)=1-|x-2|$

Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.
[Hint: 2 women occupy the chair, from 1 to 4 in ⁴P₂ ways and 3 men occupy the remaining chairs in ⁶P₃ ways.]

If Z₁, z₂, z₃ are complex numbers such that $|\text{z}_1|=|\text{z}_2|=|\text{z}_3|=\Big|\frac{1}{\text{z}_1}+\frac{1}{\text{z}_2}+\frac{1}{\text{z}_3}\Big|=1,$ then find the value of $|\text{z}_1+\text{z}_2+\text{z}_3|.$

Is $g=\{(1,1),(2,3),(3,5),(4,7)\}$ is a function? If $g$ is represented by $g(x)=\alpha x+\beta$ then find the value of $\alpha$ and $\beta$.