Question

If f : R → R and g : R → R are given by f(x) = sin x and g(x) = 5x² then find gof(x)

What is the degree of the following differential equation ? $5x\biggl(\frac{d y}{d x}\biggr)^{2}-\frac{d^{2}y}{d x^{2}}-6y\;=\log x.$

Write the degree of the differential equation : $\left(\frac{d y}{d x}\right)^{4}+3x\frac{d^{2}y}{d x^{2}}=0.$

If the determinant of matrix A of order 3 × 3 is of value 4, write the value of |3A|.

Evaluate $\textstyle\int\!{\frac{e^{2\,x}\,-\,e^{-2\,x}}{e^{2\,x}\,+\,e^{-2\,x}}}\,d x\,.$

Find the sum of the vectors : $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{i}-2\stackrel{\wedge}{j},$ $\vec{b}=2\hat{i}-3\hat{j},$ $\vec{c}=2\hat{i}+3\hat{k},$

If $\left(\begin{array}{l l }x-y & z \\ 2x-y & w\end{array}\right)$ = $\left(\begin{array}{l l }-1 & 4 \\ 0 & 5\end{array}\right)$ , find the value of x + y.