_ x 1 1 - 2(x - 1) x - 1 - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 1} \frac{{\sqrt {1 - \cos 2(x - 1)} }}{{x - 1}}$

A
Exists and it equals $\sqrt 2 $
B
Exists and it equals $ - \sqrt 2 $
C
Does not exist because $x - 1 \to 0$
✓
Does not exist because left hand limit is not equal to right hand limit

✓

Answer

Correct option: D.

Does not exist because left hand limit is not equal to right hand limit

d
(d) $f(1 + ) = \mathop {\lim }\limits_{h \to 0} f(1 + h) = \mathop {\lim }\limits_{h \to 0} \,\,\frac{{\sqrt {1 - \cos \,\,2h} }}{h}$
$ = \mathop {\lim }\limits_{h \to 0} \,\sqrt 2 \frac{{\sin \,h}}{h} = \sqrt 2 $
$f(1 - ) = \mathop {\lim }\limits_{h \to 0} f(1 - h) = \mathop {\lim }\limits_{h \to 0} \,\,\frac{{\sqrt {1 - \cos \,( - 2h)} }}{{ - h}}$
$ = \mathop {\lim }\limits_{h \to 0} \,\sqrt 2 \frac{{\sin \,h}}{{ - h}} = - \sqrt 2 .$
$\therefore $ limit does not exist because left hand limit is not equal to right hand limit.

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 STD 11 - 12. limits→STD 11 - 12. limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The equation $3\cos\text{x}+4\sin\text{x}=6$ has .... solution.

$\lim _{x \rightarrow 0} \frac{\sin x}{\sqrt{x+1}-\sqrt{1-x}}$ is equal to

Equation of line passing through $(1, 2)$ and perpendicular to $3x + 4y + 5 = 0$ is

If $\tan\text{A}+\cot\text{A}=4,$ then $\tan^4\text{A}+\cot^4\text{A}$ is equal to:

Point of intersection of the diagonals of square is at origin and coordinate axis are drawn along the diagonals. If the side is of length $a$, then one which is not the vertex of square is

Let $\mathrm{S}=\left\{x \in R:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\right\}$. Then the number of elements in $\mathrm{S}$ is :

Let $a>0, b>0$. Let $e$ and $\ell$ respectively be the eccentricity and length of the latus rectum of the hyperbola $\frac{ x ^{2}}{ a ^{2}}-\frac{ y ^{2}}{ b ^{2}}=1$. Let $e ^{\prime}$ and $\ell^{\prime}$ respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If $e ^{2}=\frac{11}{14} \ell$ and $\left( e ^{\prime}\right)^{2}=\frac{11}{8} \ell^{\prime}$, then the value of $77 a+44 b$ is equal to

If the equation $2\ {\sin ^2}x + \frac{{\sin 2x}}{2} = k$ , has atleast one real solution, then the sum of all integral values of $k$ is

If the tangents drawn at the point $O (0,0)$ and $P (1+\sqrt{5}, 2)$ on the circle $x ^{2}+ y ^{2}-2 x -4 y =0$ intersect at the point $Q$, then the area of the triangle $OPQ$ is equal to

If the digits are not allowed to repeat in any number formed by using the digits $0,2,4,6,8$, then the number of all numbers greater than $10,000$ is equal to $....$