1.State the derivative of $\sin(x)$ and $\cos(x)$ with respect to $x$.
Sol: $\frac{d}{dx}(\sin x) = \cos x$ and $\frac{d}{dx}(\cos x) = -\sin x$.
2.Evaluate the definite integral $\int_1^3 x^2 dx$.
Sol: $\int_1^3 x^2 dx = \left[ \frac{x^3}{3} \right]_1^3 = \frac{27 - 1}{3} = \frac{26}{3}$.
3.What is the formula for the roots of quadratic equation $ax^2 + bx + c = 0$?
Sol: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
4.State the small angle approximation for $\sin \theta$ and $\cos \theta$ when $\theta \ll 1$ in radians.
Sol: $\sin \theta \approx \theta$ and $\cos \theta \approx 1 - \frac{\theta^2}{2} \approx 1$.
