Brief Answer Questions: a. If A = \1, 2, 3, 4, 5\, B = \3, 4, 5, 6, 7\ and C = \1, 3, 5, 7\ , find (A B C) . b. Express the complex number 1 + i 3 into polar form. c. Rewrite 4 x 1 by using the…

Brief Answer Questions: a. If $A=\{1,2,3,4,5\},B=\{3,4,5,6,7\}$ and $C=\{1,3,5,7\}$, find $(A\cap B\cap C)$.

b. Express the complex number $-1+i\sqrt{3}$ into polar form.

c. Rewrite $-4\le x\le -1$ by using the modulus sign.

d. Evaluate: ${\lim }_{x\to \infty }\frac{5x^3+3x+7}{2x^3+7x+9}$

e. Find a unit vector perpendicular to each of the vectors $\vec{a}=\vec{i}+3\vec{j}+2\vec{k}$ and $\vec{b}=2\vec{i}-4\vec{j}+\vec{k}$

f. Find the derivative of $y=e^{2x}$

g. If $A=\left[\begin{array}{cc}2& -4\\ 4& 1\end{array}\right]$ and $B=\left[\begin{array}{cc}3& 6\\ 5& 2\end{array}\right]$, find $5(A+B)$.

h. Find the area bounded by the line $y=2x+3$, the x-axis and the ordinates at $x=2$ and $x=4$

i. Solve the different equation: $\frac{dy}{dx}=3x^2$

j. Find the value of determinant: $\left|\begin{array}{ccc}1& 3& 2\\ 3& 4& 1\\ 2& 5& 1\end{array}\right|$