Evaluate the following limit: _ x 0 3x 5x - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{5\text{x}}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{5\text{x}}$
$=\frac{1}{5}\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{3\text{x}}\times3$
$=\frac35\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{3\text{x}}$
$=\frac{3}{5}\times1$ $\Big[\because\ \lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}}{\text{x}}=1\Big]$
$=\frac{3}{5}$

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→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If A and B are two events associated with a random experiment such that P(A) = 0.5, P(B) = 0.3 and $\text{P}(\text{A}\cap\text{B})=0.2,$ find $\text{P}(\text{A}\cup\text{B}).$

In how many ways can an examinee answer a set of ten true/ false type questions?

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

Find the equation of ellipse having Centre at $(0, 0)$ major axis on the y-axis and passes through the points $(3, 2)$ and$ (1, 6) .$

Find the derivative of function $\sin x \cos x.$

State whether the two lines in the following are parallel, perpendicular or neither.
Through $(5, 6)$ and $(2, 3);$ through $(9, -2)$ and $(6, -5)$

Find the number of different signals that can be generated by arranging at least 2 flags in order (one below the other) on a vertical staff, if five different flags are available.

Convert the complex number $\frac {-16}{1+\sqrt3i}$ into polar form.

Find the area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 12y$ to the ends of its latus rectum.

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.