Evaluate _ x - 2 1 x + 1 2 x + 2 - Vidyadip

Question

Evaluate $\mathop {\lim }\limits_{x \to - 2} \frac{{\frac{1}{x} + \frac{1}{2}}}{{x + 2}}$

✓

Answer

Here $\mathop {\lim }\limits_{x \to - 2} \frac{{\frac{1}{x} + \frac{1}{2}}}{{x + 2}}$
$ = \mathop {\lim }\limits_{x \to - 2} \frac{{\frac{{x + 2}}{{2x}}}}{{x + 2}}$
$ = \mathop {\lim }\limits_{x \to - 2} \frac{{x + 2}}{{2x}} \times \frac{1}{{x + 2}}$
$ = \mathop {\lim }\limits_{x \to - 2} \frac{1}{{2x}} = \frac{1}{{2 \times - 2}} = \frac{{ - 1}}{4}$

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 and Derivatives→Limits and Derivatives — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

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.

Prove that:
$(\sin^3\text{x}+\sin\text{x})\sin\text{x}+(\cos3\text{x}-\cos\text{x})\cos\text{x}=0$

Find the number of different 8-letter arrangement that can be made from the letters of the word DAUGHTER so that all vowels occur together.

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and C(-1, -1) are the vertices of a right angled triangle.

Differentiate the following functions.
$\frac{\text{x}^{4}+\text{x}^{3}+\text{x}^{2}+1}{\text{x}}$

Insert 4 A.M.s between 4 and 19.

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum: x² = 6y

Write the distances of point $(1,2,3)$ from the coordinate axes.

How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?

Find the value of $\tan 105^{\circ}$.