Download App

CONTINUITY AND DIFFERENTIABILITY — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
If $x$ and $y$ are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.\text{x}=\sin\text{t, y}=\cos2\text{t}$
✓

Answer

The given equations are $\text{x}=\sin\text{ t and y}=\cos=2\text{t}$
Then,$\frac{\text{dx}}{\text{dt}}=\frac{\text{d}}{\text{dt}}(\sin\text{t)}=\cos\text{t}$
$\frac{\text{dy}}{\text{dt}}=\frac{\text{d}}{\text{dt}}(\cos2\text{t})=-\sin2\text{t}.\frac{\text{d}}{\text{dt}}(2\text{t})=-2\sin2\text{t}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{\Big(\frac{\text{dy}}{\text{dt}}\Big)}{\Big(\frac{\text{dx}}{\text{dt}}\Big)}=\frac{-2\sin2\text{t}}{\cos\text{t}}=\frac{-2.2\sin\text{t}\cos\text{t}}{\cos\text{t}}=-4\sin\text{t}$

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 CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the unit vector in the direction of the sum of the vectors $\vec a = 2\hat i + 2\hat j - 5\hat k$ and $\vec b = 2\hat i + \hat j + 3\hat k$.
→
Find $\frac { d y } { d x }$ of the function $(\cos x)^y = (\cos y)^x.$
→
Evaluate the following integrals:
$\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\log\Big(\frac{\text{a}-\sin\theta}{\text{a}+\sin\theta}\Big)\text{d}\theta$
→
The equations of a line are given by $\frac{4-\text{x}}{3}=\frac{\text{y}+3}{3}=\frac{\text{z}+2}{6}.$ Write the direction cosines of a line parallel to this line.
→
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that
one of them is black and other is red.
→
If f(x) = x + 7 and g(x) = x - 7, x ∈ R, write fog (7).
→
Evaluate the following integrals:
$\int\bigg\{\text{x}^2+\text{e}^{\log\text{x}}+\Big(\frac{\text{e}}{2}\Big)^\text{x}\bigg\}\text{dx}$
→
Evaluate:
$\cot\Big(\sin^{-1}\frac{3}{4}+\sec^{-1}\frac{4}{3}\Big)$
→
State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive.
→
If $\text{x}=2\text{ at},\text{y}=\text{at}^2,$ where a is a constant, then find $\frac{\text{d}^2\text{y}}{\text{dx}^2}\text{ at}\text{ x}=\frac{1}{2}.$
→