Download App

Limits — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{x}+\text{b}^\text{x}-\text{c}^\text{x}-\text{d}^\text{x}}{\text{x}}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{x}+\text{b}^\text{x}-\text{c}^\text{x}-\text{d}^\text{x}}{\text{x}}$
$=\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{x}-1}{\text{x}}+\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{x}-1}{\text{x}}-\lim\limits_{\text{x}\rightarrow0}\frac{\text{c}^\text{x}-1}{\text{x}}-\lim\limits_{\text{x}\rightarrow0}\frac{\text{d}^\text{x}-1}{\text{x}}$
$=\text{log a}+\text{log b}-\text{log c}-\text{log d}$
$=\text{log}\Big(\frac{\text{ab}}{\text{cd}}\Big)$

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 Limits→Limits — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Solve for x, the inequalities Exercises.
$|\text{x}-1|\leq5,\ |\text{x}|\geq2$
→
Is 302 a them of the A.P. 3, 8, , 13, ...?
→
Find the value of the following trigonomentric ratio:
$\cos\Big(\frac{19\pi}{6}\Big)$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow4}\frac{\text{x}^2-7\text{x}+12}{{\text{x}^2}-3\text{x}-4}$
→
Find $\mathop {\lim }\limits_{x \to 1} f(x)$ where f(x) = $\left\{ {\begin{array}{*{20}{c}} {{x^2} - 1,}&{x \le 0} \\ { - {x^2} - 1,}&{x > 1} \end{array}} \right.$
→
Two unbisased dice are thrown, find the probability that the total of the numbers on the dice is greater than 10.
→
Prove that:
$\cos\Big(\frac{3\pi}{4}+\text{x}\Big)-\cos\Big(\frac{3\pi}{4}-\text{x}\Big)=-\sqrt2\sin\text{x}$
→
Find the value of the following :
$(1+i)^8+(1-i)^8$
→
Find principal argument of $(1+\text{i}\sqrt{3})^2$
→
Sketch the graphs of the following function:
$\text{f(x)}=2\sin\text{x},0\leq\text{x}\leq\pi$
→