Continuity and Differentiability

CBSE Class 12 · Mathematics · 41 past questions

7 of 41 · show all

1. Q35 2023

   The value of k for which function $f(x) = \begin{cases} x^2, & x \geq 0 \\ kx, & x < 0 \end{cases}$ is…

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2. Q36 2023

   If $y = \frac{\cos x - \sin x}{\cos x + \sin x}$, then $\frac{dy}{dx}$ is…

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3. Q37 2023

   If $y = x^{\frac{1}{x}}$, then find $\frac{dy}{dx}$ at $x = 1$.

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4. Q38 2023

   The value of k for which $f(x) = \begin{cases} 3x+5, & x \ge 2 \\ kx^2, & x < 2 \end{cases}$ is a continuous…

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5. Q39 2023

   If $y = (x + \sqrt{x^2 - 1})^2$, then show that $(x^2 - 1)\left(\frac{dy}{dx}\right)^2 = 4y^2$.

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6. Q40 2023

   The function $f(x) = x|x|$ is

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7. Q41 2023

   If $\tan\left(\frac{x+y}{x-y}\right) = k$, then $\frac{dy}{dx}$ is equal to

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