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Continuity & Differentiability — GSEB Class 12 (HSC)

Master Continuity & Differentiability for GSEB Class 12 (HSC). Free verified step-by-step solutions, 2 past exam problems, formulas, and markschemes.

Exam Questions & Step-by-Step Markschemes (2 Problems)

Question 1 • 2024 3 Marks

          Find \frac{dy}{dx} if x^y + y^x = a^b , where a, b > 0 are constants.
        

Answer: \frac{dy}{dx} = -\frac{y x^{y-1} + y^x \ln y}{x^y \ln x + x y^{x-1}}

Question 2 • 2023 3 Marks

          Find the value of k so that the function f is continuous at x = \frac{\pi}{2} : f(x) = \begin{cases} \frac{k \cos x}{\pi - 2x}, & \text{if } x \neq \frac{\pi}{2} \\ 3, & \text{if } x = \frac{\pi}{2} \end{cases}
        

Answer: k = 6

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