MCQ_SINGLE

The value of k for which function $f(x)=\begin{cases}x^{2},&x\ge0\\ kx,&x

MCQ_SINGLE

If \(f(x)=\begin{cases}\frac{\log(1+ax)+\log(1-bx)}{x},&for~x\ne0\\ k&,for~x=0\end{cases}\) is continuous at \(x=0\), then the value of k is:

MCQ_SINGLE

For what value of k, the function given below is continuous at \(x=0\) ? \(f(x)=\begin{cases}\frac{\sqrt{4+x}-2}{x},&x\ne0\\ k,&x=0\end{cases}\)

MCQ_SINGLE

If \( f(x) = \begin{cases} 1, & \text{if } x \leq 3 \\ ax + b, & \text{if } 3 < x < 5 \\ 7, & \text{if } x \geq 5 \end{cases} \) is continuous for all real numbers, then find the values of \(a\) and \(b\):

SA

(a) Differentiate sec⁻¹(1/√(1-x²)) w.r.t. sin⁻¹(2x√(1-x²)). OR (b) If y = tan x + sec x, then prove that d²y/dx² = cos x / (1 - sin x)².

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