Evaluate the following limit: _ x 0 (a+x)^2-a^2 x - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{(\text{a}+\text{x})^2-\text{a}^2}{\text{x}}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{(\text{a}+\text{x})^2-\text{a}^2}{\text{x}}$$=\lim\limits_{\text{x}\rightarrow0}\frac{(\text{a}+\text{x}-\text{a})(\text{a}+\text{x}+\text{a})}{\text{x}}$
$=\lim\limits_{\text{x}\rightarrow0}\frac{(\text{x})(2\text{a}+\text{x})}{\text{x}}$
$=\lim\limits_{\text{x}\rightarrow0}(2\text{a}+\text{x})$
$=2\text{a}$

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 1 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

State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer. All integers are positive or negative.

Determine the distance between the following pair of parallel lines: 4x + 3y - 11 = 0 and 8x + 6y = 15

Find the value of cos (–1710°).

Determine the contrapositive of the following statements: It is necessary to be strong in order to be a sailor.

The given following sets are finite & in which of it infinite in if? Set of letters of the English Alphabets;

If the distance between the foci of an ellipse is equal to the lengh of the latus-rectum, write the eccentricity of the ellipse.

A company manufactures cassettes and its cost and revenue functions for a week are $\text{C}=300+\frac{3}{2}\text{x}$ R = 2x respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?

Prove that: $\frac{\sin x+\sin 3 x}{\cos x+\cos 3 x}=\tan 2 x$

Write the coordinates of the point P which is five-sixth of the way from A(-2, 0, 6) to B(10, -6, -12).

Write the value of $\cos1^\circ+\cos2^\circ+\cos3^\circ+\ ...\ +\cos180^\circ.$