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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 $\frac{\text{dy}}{\text{dx}}.x = 2at^2, y = at^4$
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Answer

The given equations are $x = 2at^2$ and $y = at^4$
Then, $\frac{\text{dx}}{\text{dt}}=\frac{\text{d}}{\text{dt}}(2\text{at}^2)=2\text{a}.\frac{\text{d}}{\text{dt}}(\text{t}^2)=4\text{at}$ and $\text{y}=\text{at}^4$
$\frac{\text{dx}}{\text{dt}}=\frac{\text{d}}{\text{dt}}(\text{at}^4)=\text{a}\frac{\text{d}}{\text{dt}}\text{(t}^4)=\text{a}.4.\text{t}^3=4\text{at}^3$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{\Big(\frac{\text{dy}}{\text{dt}}\Big)}{\Big(\frac{\text{dx}}{\text{dt}}\Big)}=\frac{4\text{at}^3}{4\text{at}}=\text{t}^2$

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