\begin{align} \int \frac {sec^2 x}{Coses^2 x} . dx\end{align}
\begin{align} =\int \left(\frac{\frac {1}{Cos^2 x}}{\frac{1}{sin^2 x}}\right) . dx\end{align}
\begin{align} =\int \left(\frac{Sin^2x}{Cos^2x}\right) . dx\end{align}
\begin{align} =\int tan^2 x . dx\end{align}
\begin{align} =\int \left(sec^2x - 1\right) . dx\end{align}
\begin{align} =\int sec^2x . dx - \int 1. dx\end{align}
\begin{align} = tanx - x + C\end{align}
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
Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
(A) 10π (B) 12π (C) 8π (D) 11π
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
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 = ex +1 : yn -y' = 0