Mathematics Tes...

The derivative of sin^-1 (2x² - 1) w.r.t sin^-1 x is

Consider the following statements in respect of the differential equation

$\frac{d^{2}y}{d{x}^2}+\cos \left(\frac{dy}{dx}\right)=0$

1. The degree of the differential equation is not defined.

2. The order of the differential equation is 2

Which of the above statements is correct?

In the following trigonometry expression, find the value of (MN).

\(\frac{(1+\cos x)}{(1-\sin x)}(\sin x+\cos x-1)^{2}=M \sin ^{N} x\)

Find the equation of line through (-4,1,3) and parallel to the plane \(x+y+z=3\) while the line intersects another line whose equation is \(x+y-z=0=x+2 y-3 z+5\):

Evaluate: \(\lim _{\mathrm{x} \rightarrow \infty} \mathrm{x}^{\frac{2}{\mathrm{x}}}=?\)

The slope of the tangent at \((x, y)\) to a curve passing through \(\left[1,\left(\frac{\pi}{4}\right)\right]\) is given by \(\left(\frac{y}{x}\right)-\cos ^{2}\left(\frac{y}{x}\right)\), then the equation of the curve is:

The value of \([\vec{a} \vec{b}+\vec{c} \vec{a}+\vec{b}+\vec{c}]\) is:

What should be the value of k such that the function \(\mathrm{f}(\mathrm{x})=\left\{\begin{array}{ccc}\frac{k \sin (\pi-x)}{\pi-x} & \text { if } & x \neq \pi \\ 1 & \text { if } & x=\pi\end{array}\right.\) is continuous at \(x=\pi\).

Find the real and imaginary part of the complex number \(z=\frac{1-i}{1+i}\).