Mathematics Tes...

Find the intervals in which the function f(x) is increasing , where f(x) is given by:

f(x) = sin x + cos x, 0 ≤ x ≤ 2π

Solve the differential equation \(\frac{d y}{d x}+y \cos x=3 \cos x\).

The number of spheres that can be made to pass through the three given points (1,0,0), (0,1,0) and (0,0,1) is:

Find the value of \(\int \frac{d x}{\sqrt{(x+1)(x+2)}}\)

Find \(\int\left(e^{x \log a}+e^{a \log x}+e^{a \log a}\right) d x\)

The value of the integral \(\int_{0}^{1.5}\left[\mathrm{x}^{2}\right] \mathrm{dx},\) where \([\mathrm{x}]\) denotes the greatest integer \(\leq \mathrm{x},\) equals (approx.):

What is the general solution of the differential equation \(x^{2} d y+y^{2} d x=0\)?

Find the differential coefficient of \(\tan ^{-1} \frac{x}{\sqrt{\left(a^{2}-x^{2}\right)}}\).

If the roots of the equation \(3 a x^{2}+2 b x+c=0\) are in the ratio \(3: 2\), then which one of the following is correct?

Integrating factor of \(\left(1-x^2\right) \frac{d y}{d x}-x y=1\) is: