The anti derivative of sin 2x – 4e3x is the function of x whose derivative is sin 2x – 4e3x.
It is known that,
\begin{align} \frac {d}{dx} \left(-\frac{1}{2}cos 2x – \frac {4}{3} e^{3x}\right) = sin2x – 4e^{3x} \end{align}
Therefore, the anti derivative of (sin 2x – 4e3x) is \begin{align} \left(-\frac{1}{2}cos 2x – \frac {4}{3} e^{3x}\right) \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).
y = cosx + C : y' + sinx = 0
Let f : N → N be defined by
State whether the function f is bijective. Justify your answer.
Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one.
Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
Find gof and fog, if
(i) f(x) = | x | and g(x) = | 5x – 2 |
(ii) f(x) = 8x3 and g(x) = x1/3 .
Classify the following measures as scalars and vectors.
(i) 10 kg (ii) 2 metres north-west (iii) 40°
(iv) 40 watt (v) 10–19 coulomb (vi) 20 m/s2
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x2