Question

Write the projection of the vector $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ along the vector $\stackrel{\rightarrow}{j}\$.

Find matrix A such that. $\left(\begin{array}{l l}{2}&{-1}\\ {1}&{0}\\ {-3}&{4}\end{array}\right)$ $A={\left(\begin{array}{l l}{-1}&{-8}\\ {1}&{-2}\\ {9}&{22}\end{array}\right)}$

If $A_{i j}$ is the cofactor of the element $a_{i j}$ of the determinant $\begin{vmatrix}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{vmatrix}$ , then write the value of $a_{32}A_{32}.$

Find the slope of tangent to the curve y = 3x² – 6 at the point on it whose x-coordinate is 2.

Find : $\textstyle\int{\frac{\sin^{6}x}{\cos^{8}x}}\,d x.$

Write the equation of tangent drawn to the curve y = sin x at the point (0, 0).

Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} given by f = {(1, 2) (3, 5) (4, 1)} and g = {(1, 3), (2, 3), (5, 1)} Write down gof.