Evaluate the following limits: _ x 3x^ -1 +4x^ -2 5x^ -1 +6x^ -2 - Vidyadip

Question

Evaluate the following limits: $\lim\limits_{\text{x}\rightarrow\infty}\frac{3\text{x}^{-1}+4\text{x}^{-2}}{5\text{x}^{-1}+6\text{x}^{-2}}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow\infty}\frac{3\text{x}^{-1}+4\text{x}^{-2}}{5\text{x}^{-1}+6\text{x}^{-2}}$ $=\lim\limits_{\text{x}\rightarrow\infty}\frac{\frac{3}{\text{x}}+\frac{4}{\text{x}^2}}{\frac{5}{\text{x}}+\frac{6}{\text{x}^2}}$ $\Big[\frac{0}{0}\text{ from}\Big]$ $=\lim\limits_{\text{x}\rightarrow\infty}\frac{\frac{1}{\text{x}}\big(3+\frac{4}{\text{x}}\big)}{\frac{1}{\text{x}}\big(5+\frac{6}{\text{x}}\big)}$ $=\lim\limits_{\text{x}\rightarrow\infty}\frac{(3+0)}{(5+0)}=\frac35$

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 3 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 mean deviation about the median for the data in: $13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17.$

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x + y = 16.

Find the mean deviation about the median for the following data.

$x_i$	3	6	9	12	13	15	21	22
$f_i$	3	4	5	2	4	5	4	3

Find what the following equations become when the origin is shifted to the point $(1, 1). xy − y^2 − x + y = 0$

Find the magnitude, in radians and degrees, of the interior angle of a regular. Pentagon

Prove that $\cos\frac{\pi}{5}\cos\frac{2\pi}{5}\cos\frac{\pi}{5}\cos\frac{8\pi}{5}=\frac{-1}{16}$

Find the coordinates of the foot of perpendicular from the point (-1, 3) to the line 3x - 4y - 16 = 0

Let A = {x : x $\in$ N}, B = {x : x = 2n, n $\in$ N}, C = {x : x = 2n - 1, n $\in$ N} and D = {x : x is a prime natural number}. Find: $\text{C}\cap\text{D}$

Find the domain and range of the following real valued functions: f(x) = |x - 1|

For any two complex numbers $z_1$ and $z_2$, prove that $\operatorname{Re}\left(z_1 z_2\right)=\operatorname{Re}\left(z_1\right) \operatorname{Re}\left(z_2\right)-\operatorname{Im}\left(z_1\right) \operatorname{Im}\left(z_2\right)$.