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 $\frac{\text{dy}}{\text{dx}}.$
$\text{x}=4\text{t, y}=\frac{4}{\text{t}}$
✓

Answer

The given equations are $\text{x}=4\text{t, and y}=\frac{4}{\text{t}}$
$\frac{\text{dx}}{\text{dt}}=\frac{\text{d}}{\text{dt}}(4\text{t)}=4$
$\frac{\text{dy}}{\text{dt}}=\frac{\text{d}}{\text{dt}}\Big(\frac{4}{\text{t}}\Big)=4.\frac{\text{d}}{\text{dt}}\Big(\frac{1}{\text{t}}\Big)=4.\Big(\frac{-1}{\text{t}^2}\Big)=\frac{-4}{\text{t}^2}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{\Big(\frac{\text{dy}}{\text{dt}}\Big)}{\Big(\frac{\text{dx}}{\text{dt}}\Big)}=\frac{\Big(\frac{-4}{\text{t}^2}\Big)}{4}=\frac{-1}{\text{t}^2}$

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

Let $f, g : R \rightarrow R$ be defined by $f(x) = 2x + 1$ and $g(x) = x^2 - 2$ for all $x \in R,$ respectively. Then, find $gof.$
→
Write the general equation of a plane parallel to X-axis.
→
Answer each of the following questions in one word or one sentence or as per exact requirement of the quetion:
Find the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane $\vec{\text{r}}.(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}})=2.$
→
If $A$ is a non$-$singular square matrix such that $|A| = 10,$ find $|A^{-1}|.$
→
Evaluate the following:
$\tan\Big(\cos^{-1}\frac{8}{17}\Big)$
→
Write the value of the determinant $\begin{vmatrix}\text{a}&1&\text{b}+\text{c}\\\text{b}&1&\text{c}+\text{a}\\\text{c}&1&\text{a}+\text{b}\end{vmatrix}$
→
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors of the same magnitude inclined at an angle of $60^\circ$ such that $\vec{\text{a}}.\vec{\text{b}}=8,$ write the value of their magnitude.
→
If $F(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$, show that $\mathrm{F}(\mathrm{x}) \mathrm{F}(\mathrm{y})=\mathrm{F}(\mathrm{x}+\mathrm{y})$
→
Evaluate the following integral:
$\int\frac{1}{\sqrt{\text{a}^2-\text{b}^2\text{x}^2}}\text{ dx}$
→
Write the cofactor of $a_{12}$ in the following matrix $\begin{bmatrix}2&-3&5\\6&0&4\\1&5&-7\end{bmatrix}$
→