L9 Continuity and Differentiability

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सफर में मुश्किलें आऐ, तो हिम्मत और बढ़ती है।
कोई अगर रास्ता रोके, तो जुर्रत और बढ़ती है।
अगर बिकने पे आ जाओ, तो घट जाते हैं दाम अक्सर।
ना बिकने का इरादा हो तो, कीमत और बढ़ती है।

Lecture - 9 Chapter 5 Continuity and Differentiability

In this lecture, I am discussing about parametric functions and questions from NCERT Exercise 5.6 which are based on differentiation of parametric functions.

Questions discussed in this lecture:

NCERT EXERCISE 5.6 (Parametric Functions)

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find \( \frac{dy}{dx} \).

Question 1. \( x = 2at^2, y = at^4 \)

Question 2. \( x = a \cos \theta, y = b \cos \theta \)

Question 3. \( x = \sin t, y = \cos 2t \)

Question 4. \(  x = 4t, y = \frac{4}{t} \)

Question 5. \( x = \cos \theta – \cos 2\theta, y = \sin \theta – \sin 2\theta \)

Question 6. \( x = a( \theta – \sin \theta), y = a (1 + \cos \theta) \)

Question 7. \( x = \frac{\sin^3{t}}{\sqrt{\cos 2t}},  y = \frac{\cos^3{t}}{\sqrt{\cos 2t}} \)

Question 8. \( x = a \left( \cos t + log \tan \frac{t}{2} \right ), y = a \sin t \)

Question 9. \( x = a \sec \theta, y = b \tan \theta \)

Question 10. \( x = a(\cos \theta + \theta \sin \theta), y = a(\sin \theta – \theta \cos \theta) \)

Question 11. If \( x = \sqrt{a^{\sin^{-1}t}},  y = \sqrt{a^{\cos^{-1}t}}\), show that \( \frac{dy}{dx} = -\frac{y}{x} \).

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