Download App

Limits — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{3^{2+\text{x}}-9}{\text{x}}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{3^{2+\text{x}}-9}{\text{x}}=\lim\limits_{\text{x}\rightarrow0}\frac{3^2.3^\text{x}-9}{\text{x}}$
$=9\lim\limits_{\text{x}\rightarrow0}\frac{3^\text{x}-1}{\text{x}}$
$=9 \text{log}_\text{e}3$

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

Express the following complex numbers in the standard form a + ib:
$(1+\text{i})(1+2\text{i})$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{1-\cos2\text{x}}{3\tan^2\text{x}}$
→
Prove that :
$\frac{\sin (A-B)}{\cos A \cos B}+\frac{\sin (B-C)}{\cos B \cos C}+\frac{\sin (C-A)}{\cos C \cos A}=0$
→
If three points A(h, 0), P(a, b) and B(0, k) lie on a line, show that:
$\frac{\text{a}}{\text{h}}+\frac{\text{b}}{\text{k}}=1.$
→
If equation of parabola $y^2=8 x$, then find the coordinates of focus, axis, equation of directrix and length of latus rectum.
→
There are n A.M.s between 3 and 17. The ratio of the last mean to the first mean is 3 : 1. Find the value of n.
→
How many 3-digit numbers are there, with distinct digits, with each digit odd?
→
Find the equation of the ellipse which has Vertices (0, $\pm$13), foci(0, $\pm$5)
→
Prove thart.
$\frac{1}{9!}+\frac{1}{10!}+\frac{1}{11!}=\frac{122}{11!}$ 
→
A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?
→