Download App

12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to a} \frac{{\cos x - \cos a}}{{\cos x - \cot a}} = $
  • A
    $\frac{1}{2}{\sin ^3}a$
  • B
    $\frac{1}{2}{\rm{cose}}{{\rm{c}}^2}a$
  • ✓
    ${\sin ^3}a$
  • D
    ${\rm{cose}}{{\rm{c}}^3}a$
✓

Answer

Correct option: C.
${\sin ^3}a$
c
(c) $\mathop {\lim }\limits_{x \to a} \,\frac{{\cos x - \cos a}}{{\cot x - \cot a}} = \mathop {\lim }\limits_{x \to a} \,\left( {\frac{{ - \sin x}}{{ - \cos e{c^2}x}}} \right) $

$= \mathop {\lim }\limits_{x \to a} {\sin ^3}x = {\sin ^3}a$.

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 "MCQ" from 12. limits→12. limits — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Choose the correct answer. $\cos2\theta\cos2\phi+\sin^2(\theta-\phi)-\sin^2(\theta+\phi)$ is equal to:
[Hint: Use $\sin^2\text{A}-\sin^2\text{B}=\sin(\text{A+B})\sin(\text{A}-\text{B})$]
→
Let $\text{A} = \{\text{x : x} \in \text{R}, \text{x > 4}\}$ and $\text{B}= \{\text{x}\in\text{R : x} < 5\}.$ Then, $\text{A}\cap\text{B}=$
→
The probability that at least one of the events $A$ and $B$ occurs is $3/5$. If $A$ and $B$ occur simultaneously with probability $1/5$, then $P(A') + P(B')$ is
→
From a pack of $52$ cards one card is drawn at random, the probability that it is either a king or a queen is
→
Equation of the circle which touches the lines $x = 0,\;y = 0$ and $3x + 4y = 4$ is
→
Two dice are thrown independently. Let $A$ be the event that the number appeared on the $1^{\text {st }}$ die is less than the number appeared on the $2^{\text {nd }}$ die, $B$ be the event that the number appeared on the $1^{\text {st }}$ die is even and that on the second die is odd, and $C$ be the event that the number appeared on the $1^{\text {st }}$ die is odd and that on the $2^{\text {nd }}$ is even. Then
→
If $cosA + cosB = cosC,\ sinA + sinB = sinC$ then the value of expression $\frac{{\sin \left( {A + B} \right)}}{{\sin 2C}}$ is
→
If 4-digit numbers greater than 5000 are randomly formed from the digits 0, 1, 3, 5 and 7, then the probability of forming a number divisible by 5 when the digits are repeated is:
→
If $\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\ldots+\frac{1}{\sqrt{99}+\sqrt{100}}=m$ and $\frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\ldots+\frac{1}{99 \cdot 100}=\mathrm{n}$, then the point $(\mathrm{m}, \mathrm{n})$ lies on the line
→
If (-4, 5) is one vertex and 7x - y + 8 = 0 is onediagonal of a square, then the equation of second diagonal is:
→