Evaluate the following limit: _ x 0 ^23x x^2 - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\tan^23\text{x}}{\text{x}^2}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\tan^23\text{x}}{\text{x}^2}$ $=\Big(\lim\limits_{\text{x}\rightarrow0}\frac{\tan3\text{x}}{\text{x}}\Big)^2$ $=\Big(\lim\limits_{\text{x}\rightarrow0}\frac{\tan3\text{x}}{3\text{x}}\Big)^2$ $=1\times9$ $\Big[\because\ \lim\limits_{\text{x}\rightarrow0}\frac{\tan\text{x}}{\text{x}}=1\Big]$ $=9$

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

If $\left(\frac{1+i}{1-i}\right)^{m} = 1$ then find the least positive integral value of m.

If the origin is the centriod of the triangle PQR with vertices P(2a, 2, 6), Q(-4, 3b, -10) and R(8, 14, 2c), then find the values of a, b and c.

Find the distance between parallel lines. l(x + y) + p = 0 and l(x + y) - r = 0

Show that the set of letters needed to spell CATARACT and the set of letters needed to spell TRACT are equal.

Find the sum of all integers between 84 and 719, which are multiples of 5.

Find x in the following. $\frac{\text{x}}{10!}=\frac{1}{8!}+\frac{1}{9!}$

Find the distance of the point (3, -5) from the line 3x - 4y - 26 = 0

Find the derivative of. $\text{x}^{-3}(5+3\text{x})$

By using the concept of equation of a line, prove that the three points (-2, -2), (8, 2) and (3, 0) are collinear.

In how many ways can 5 different balls be distributed among three boxes?