. The Upward velocity of a rocket is given as a function at the time t , using the quadratic spline find:
i. The velocity at $t=16s$
ii. The acceleration at $t=16s$
iii. The distance covered between $t=11s$ and $t=16s$
t 0 10 15 20 22.5 30 $V(t)$ 0 227.04 362.78 517.35 602.97 901.67
2. Using Hermite's interpolation formula, find $f(2.7)$
x $f(x)$ 2 0.69315 0.5 2.5 0.91629 0.4 3 1.09861 0.33333
3. From the table below. Find a root of an equation $f(x)=x^{3}-2x-5$ using
x 10 1 2 3 $f(x)$ $-5$ $-6$ $-1$ 16
i. False Position method
ii. Newton method
iii. Secant method
iv. Bisection method