Evaluate the following limit: _ x 2 x^4-16 x -2 - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow2}\frac{\text{x}^4-16}{{\text{x}}-2}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow2}\frac{\text{x}^4-16}{{\text{x}}-2}$
$=\lim\limits_{\text{x}\rightarrow2}\frac{\big(\text{x}^2+4\big)\big(\text{x}^2+4\big)}{({\text{x}}-2)}$
$=\lim\limits_{\text{x}\rightarrow2}\frac{(\text{x}-2)(\text{x}+2)\big(\text{x}^2+4\big)}{({\text{x}}-2)}$
$=\lim\limits_{\text{x}\rightarrow2}{(\text{x}+2)\big(\text{x}^2+4\big)}$
$=(2+2)(4+4)$
$=4(8)$
$=32$

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

Similar questions

Four persons are chosen at random from a group of 4 males, 3 females and 5 children. Find the probability that exactly two of them are children.

Solve the inequality 2 (2x + 3) – 10 < 6 (x – 2) for real x.

Let N be the set of natural numbers and the relation R be defined on N such that R = {(x, y) : y = 2x, x, y $\in$ N}. What is the domain, codomain and range of R? Is this relation a function?

Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x - 7y + 5 = 0 and 3x + y = 0

Prove that:
$\sin50^\circ+\sin10^\circ=\cos20^\circ$

Find the area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the ends of its latus rectum.

A card is drawn at random from a pack of 52 cards, find the probability that the card drawn is:

A diamond card

Express the complex number ${\left( {\frac{1}{3} + 3i} \right)^3}$ in the form of a + ib.

Prove that $\cos \left( {\frac{{3\pi }}{4} + x} \right) - \cos \left( {\frac{{3\pi }}{4} - x} \right) = - \sqrt 2 \sin x$

Prove that:
$\sin47^\circ+\cos77^\circ=\cos17^\circ$