MCQ
The function $\text{f(x)}=\sin^{-1}(\cos\text{x})$ is :
- ADiscontinuous at $x = 0$
- ✓Continuous at $x = 0$
- CDifferentiable at $x = 0$
- DNone of these.
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$x = 1 + xy\frac{{dy}}{{dx}} + \frac{{{{\left( {xy} \right)}^2}}}{{2!}}{\left( {\frac{{dy}}{{dx}}} \right)^2} + \frac{{{{\left( {xy} \right)}^3}}}{{3!}}{\left( {\frac{{dy}}{{dx}}} \right)^3} + ......$ is
| Column $I$ | Column $II$ |
| $(A)$ $\int_{-1}^1 \frac{\mathrm{dx}}{1+\mathrm{x}^2}$ | $(p)$ $\frac{1}{2} \log \left(\frac{2}{3}\right)$ |
| $(B)$ $\int_0^1 \frac{\mathrm{dx}}{\sqrt{1-\mathrm{x}^2}}$ | $(q)$ $2 \log \left(\frac{2}{3}\right)$ |
| $(C)$ $\int_2^3 \frac{\mathrm{dx}}{1-\mathrm{x}^2}$ | $(r)$ $\frac{\pi}{3}$ |
| $(D)$ $\int_1^2 \frac{d x}{x \sqrt{x^2-1}}$ | $(s)$ $\frac{\pi}{2}$ |