1. Algebraically determine the behavior of fo° 412dx. Select the correct answer: • A. Diverges • B. None of these • C. Converges to - ⚫ D. Converges to ⚫ E. Converges to

Find the maximum and minimum values of the function ?(?)=10sin(?)cos(?)+11 on the interval [0,?/2] by comparing values at the critical points and endpoints.

The position of an object S(t) at any time t , is given by:

Which of the following is an expression for the arc length of the curve r(t) = <2t^2 + 1, 2t^2 −1,t^3> over the interval 0 ≤ t ≤ 3?

Find the limit (sin(6t) / t i + e^-t j +4k)

Q1:Write (T) or (F) for the following, ,then correct the wrong one. 1- The sum of a geometric series with a=1/9 and r=1/3 equal to 1/12. 2- The sequence (1+1/n)^n diverges by the root test to (1). 3- The sequence (1+(-1)^n ) converges. 4- The speed of the velocity vector has a magnitude and direction. 5- The two parallel planes have a line of intersection. 6- Simplified component equation of the plane is Ax+By+Cz=D. 7- We calculate the cross product as a determinant. 8- The directional derivative is a number. 9- The mixed second order partial derivatives of f(x,y) denoted as f_xy or f_yx. 10- f_xx=∂/∂x (∂f/∂y).

2. A HALO jumper with a mass of m parachutes from a gas balloon at time t =0. Under certainassumptions, the distance, s(t), that he has fallen in time t is given by(a) Find s′(0)and s′′(0)and interpret the quantities in terms of the HALO jumper.(b) Relate the units of s′(t)and s′′(t)to the units of t and s(t).

A stone, projected vertically upward with initial velocity 112ft/sec, moves according to s = 112t − 16t2, where s is the distance from the ground. When will it reach the maximum height?

An object moves on a trajectory given by r(t)=<10cos4t,10sin4t> for 0≤t≤π. How far does it​ travel?

A circuit has an electromotive force of E = 20sin5t V in series, a resistance of R = 5 and a capacitor C = 0.02 F. If the initial charge is q = 4 coulombs, find the charge at time t> 0.