What is the value _ x 4 x^2-2x-8 x-4 : - Vidyadip

MCQ

What is the value $ \lim_{\text{x} \rightarrow 4}\frac{\text{x}^2-2\text{x}-8}{\text{x}-4}$ :

A
$0$
B
$2$
C
$8$
✓
$6$

✓

Answer

Correct option: D.

$6$

The denominator becomes $0,$ as $x$ approaches $4.$
$ \lim_{\text{x} \rightarrow 4}\frac{\text{x}^2-2\text{x}-8}{\text{x}-4}$
Here, if we factorize the numerator we get
$ \lim_{\text{x} \rightarrow 4}\frac{(\text{x}-4) (\text{x}+2)}{\text{x}-4}$
We can now cancel out $(x - 4)$ from both the numerator and denominator.
We get, $ \lim_{\text{x} \rightarrow 4}(\text{x}+2)=6$

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 "M.C.Q (1 Marks)" from Limits and Derivatives→Limits and Derivatives — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If the sum of the binomial coefficients of the expansion $\Big(2\text{x}+\frac{1}{\text{x}}\Big)^{\text{n}}$ is equal to $256,$ then the term independent of $x$ is:

If $|x| < -5$ then the value of $x$ lies in the interval:

Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, $\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$ from any of its foci?

Let $\tan (2\pi \left| {\sin \,\theta } \right|) = \cot (2\pi \left| {\cos \,\theta } \right|),$ where $\theta \in R$ and $f(x) = (\left| {\sin \,\theta } \right| + \left| {\cos \,\theta } \right|).$ The value of $\mathop {\lim }\limits_{x \to \infty } \left[ {\frac{2}{{f(x)}}} \right]$ equals (Here $[\,]$ represents greatest integer function)

If one of the diameters of the circle $x^{2}+y^{2}-2 x-6 y+6=0$ is a chord of another circle $'C'$, whose center is at $(2,1),$ then its radius is..........

Choose the correct answer: The negation of the statement.
$“101$ is not a multiple of $3”$ is.

$\text{If}\ \sin\alpha+\sin\beta=\text{a}\text{ and }\cos\alpha-\cos\beta=\text{b},\ \text{than }\tan\frac{\alpha-\beta}{2}=$

There are $5$ apples, $4$ mangoes, $3$ oranges and $1$ each of $2$ other varieties of fruits. The number of ways of selecting at least one fruit of each kind is

If $e_1 $ is the eccentricity of the conic $9x^2 + 4y^2 = 36$ and $e_2 $ is the eccentricity of the conic $9x^2 − 4y^2 = 36,$ then

Out of $800$ boys in a school $224$ played cricket, $240$ played hockey and $236$ played basketball. Of the total $64$ played both basketball and hockey, $80$ played cricket and basketball and $40$ played cricket and hockey, $24$ players all the three games. The number of boys who did not play any game is: