\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.
Show that the Signum Function f : R → R, given by
is neither one-one nor onto.
The total revenue in Rupees received from the sale of x units of a product is given by
R (x) = 13x2 + 26x + 15
Find the marginal revenue when x = 7.
Find the direction cosines of a line which makes equal angles with the coordinate axes.