Question

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

Write the value of x + y + z if $\left(\begin{array}{l l l }1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right)$ $\left(\begin{array}{l }x \\ y \\ z\end{array}\right)$ = $\left(\begin{array}{l }1 \\ -1 \\ 0\end{array}\right)$.

If $\left(\begin{array}{l l }x-y & 2y \\ 2y+z & x+y\end{array}\right)$ = $\left(\begin{array}{l l }1 & 4 \\ 9 & 5\end{array}\right)$

Write the sum of the order and degree of the differential equation $1+\left(\frac{d y}{d x}\right)^{4}=7\left(\frac{d^{2}y}{d x^{2}}\right)^{3}\,.$

Write value of $\textstyle\int$ sec x(sec x + tan x) dx

Find the sum of the vectors $\stackrel{\rightarrow}{a}=\hat{i}-2\hat{j}+\hat{k}\;,$ $\vec{b}=-2\hat{i}+4\hat{j}+5\hat{k}$ and $\stackrel{\rightarrow}{c}=\hat{i}-6\hat{j}-7\hat{k}.$

If 2 $\left(\begin{array}{l l }3 & 4 \\ 5 & x\end{array}\right)$ + $\left(\begin{array}{l l }1 & y \\ 0 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 0 \\ 10 & 5\end{array}\right)$ find x - y.