Download App

Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{8^\text{x}-2^\text{x}}{\text{x}}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{8^\text{x}-2^\text{x}}{\text{x}}$ $=\lim\limits_{\text{x}\rightarrow0}\frac{8^\text{x}-1}{\text{x}}-\lim\limits_{\text{x}\rightarrow0}\frac{2^\text{x}-1}{\text{x}}$ $=\text{log8}-\text{log2}$ $=\text{log4}$

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

Find the sum of the following series to infinit:$10-9+8.1-7.29+\ ...\infty$
→
Find the equation of a line passing through (3, -2) and perpendicular to the line x - 3y + 5 = 0.
→
Represent the complex number z = 1 + $i \sqrt { 3 }$ in the polar form.
→
Prove that: $1+\cos^22\text{x}=2(\cos^4\text{x}+\sin^4\text{x})$
→
An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once Find the sample space.
→
Find the sum of the following arithmetic progression: a + b, a - b, a - 3b, ... to 22 terms.
→
Find the equation of the parabola that satisfies the given conditions: Focus (6, 0) directrix x = -6
→
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas: $y^2 = 8x.$
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\sin5\text{x}}{\tan3\text{x}}$
→
A card is drawn at random from a pack of 52 cards, find the probability that the card drawn is: A black king.
→