\begin{align} Let \;\; cosec^{-1}\left({-\sqrt2}\right)=y \;\;Then\;\; cosec y = -{\sqrt2} =- cosec\left(\frac{\pi}{4}\right) = cosec\left(-\frac{\pi}{4}\right)\end{align}
We know that the range of the principal value branch of cosec−1 is
\begin{align} \left[-\frac{\pi}{2},\frac{\pi}{2}\right] - \left(0 \right) and \;\;cosec\left(-\frac{\pi}{4}\right) = -\sqrt2.\end{align}
Therefore, the principal value of
\begin{align} cosec^{-1}\left(-\sqrt2\right) is -\frac{\pi}{4}\end{align}
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
Represent graphically a displacement of 40 km, 30° east of north.
If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
Show that the Signum Function f : R → R, given by
is neither one-one nor onto.
Determine order and degree(if defined) of differential equation yn + (y')2 + 2y =0
If f: R → R be given by f(x) = , then fof(x) is
(A)
(B) x3
(C) x
(D) (3 – x3).
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
Determine order and degree(if defined) of differential equation ym + 2yn + y' =0
\begin{align} y= \sqrt{1+x^2} : y^{'}=\frac{xy}{1+x^2}\end{align}
The total cost C (x) in Rupees associated with the production of x units of an item is given by
C(X) = 0.007 x3 - 0.003x2 + 15x + 4000
Find the marginal cost when 17 units are produced.
Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
Determine order and degree(if defined) of differential equation \begin{align}\frac{d^2y}{dx^2}=\cos3x + sin3x\end{align}