代写Calculus 1: Practice Midterm 2代写数据结构语言程序

Calculus 1: Practice Midterm 2

1. Compute the following.

(a) f' (x) where f(x) = sin(2x)ln(x).

(b) f'' (1) where f(x) = e 3x + x/1

2. Below is the graph of the derivative f 0 (x) of a function f(x) defined on (0, 5).

(a) What are the critical points of f(x)? Which are local minima and which are local maxima?

(b) Find the inflection points of the graph of f(x).

(c) Find an x (any x) at which the graph of f(x) is increasing and concave down.

3. Calculate

4. (10 points) The kinetic energy of an object is given by the formula

where m is its mass and is v its velocity. The standard unit for K is joules, for m is kilograms, and for v is meters per second.

(a) Suppose a rocket of mass 3 x 106 kilograms is moving at the speed of 5 x 103 meters per second and is generating kinetic energy at the rate of 60 x 1011 x 103 joules per second. At that moment, what the rate of change of its velocity?

(b) Use linear approximation to estimate the velocity after 2 seconds.

5. We want to calculate 3p4 using Newton’s method. Write a function whose root is 3p4, and execute the first two steps of Newton’s method starting with the initial guess x0 = 1.

6. Suppose Coca Cola were to design its cylindrical Coke can so that it held 100p ml soda and used the minimum amount of metal. What would be the the radius of the optimum can?