\begin{align} \int \frac{x^3 - x^2 + x - 1}{x-1} . dx\end{align}
On dividing, we obtain
\begin{align} =\int \left({x^2 + 1}\right) . dx \end{align}
\begin{align} =\int {x^2} . dx + \int 1 .dx \end{align}
\begin{align} =\frac {x^3}{3} + x + C \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).
Letbe a function defined as
. The inverse of f is map g: Range
(A)
(B)
(C)
(D)
Determine order and degree(if defined) of differential equation \begin{align}\left(\frac{ds}{dt}\right)^4\;+\;3s\frac{d^2s}{dt^2}\;=\;0\end{align}
Consider f : {1, 2, 3} → {a, b, c} given by f(1) = a, f(2) = b and f(3) = c. Find f –1 and show that (f –1)–1 = f.
Find gof and fog, if
(i) f(x) = | x | and g(x) = | 5x – 2 |
(ii) f(x) = 8x3 and g(x) = x1/3 .
The vertices of ΔABC are A (3, 5, −4), B (−1, 1, 2), and C (−5, −5, −2).
Determine order and degree(if defined) of differential equation (ym)2 + (yn)3 + (y')4 + y5 =0
Represent graphically a displacement of 40 km, 30° east of north.
y = Ax : xy' = y (x ≠ 0)