Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
The area of the region bounded by the curve, y2 = x, the lines, x = 1 and x = 4, and the x-axis is the area ABCD.
\begin{align}Area \;of\; ABCD = \int_{1}^{4} y.dx \end{align}
\begin{align} = \int_{1}^{4} \sqrt{x}.dx \end{align}
\begin{align} =\left[\frac{x^\frac{3}{2}}{\frac{3}{2}}\right]_1^4 \end{align}
\begin{align} =\frac{2}{3}\left[(4)^\frac{3}{2} - (1)^{\frac{3}{2}}\right] \end{align}
\begin{align} =\frac{2}{3}\left[8 -1\right] \end{align}
\begin{align} =\frac{14}{3}\; Units \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
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).
y = Ax : xy' = y (x ≠ 0)
A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.
Show that the Signum Function f : R → R, given by
is neither one-one nor onto.
Show that the function f : R* → R* defined by f(x) = 1/x is one-one and onto,where R* is the set of all non-zero real numbers. Is the result true, if the domain R* is replaced by N with co-domain being same as R* ?
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