10 Short Answer Calculus

I need support with this Calculus question so I can learn better.

1.

Write and then solve for the differential equation for the statement: “The rate of change of y with respect to x is inversely proportional to y2.” (10 points)

2.

Solve the differential equation dy dx equals the quotient of y times the cosine of x and the quantity 1 plus y squared with the initial condition y(0) = 1. (10 points)


3.

a. Solve the differential equation y prime equals the product of 4 times x and the square root of the quantity 1 minus y squared
b. Explain why the initial value problem y prime equals the product of 4 times x and the square root of the quantity 1 minus y squared with y(0) = 4 does not have a solution.


4.

The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of the integral from 1 to 2 of f of x, dx . Give 3 decimal places for your answer. (10 points)

x 1 1.1 1.2 1.5 1.7 1.9 2.0
f(x) 1 2 4 6 7 9 10


5.

Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 0 to 8 of x squared, dx . (10 points)

1.

The figure below shows the graph of f ‘, the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4.

Graph of a function on the domain negative 2, 6 and range negative 3, 4. Graph increases from negative 2, 3 until 2, 0 and from 4, negative 2.5 to 6, 4. Graph decreases from 2, 0 to 4, negative 2.5. There are x intercepts at 2, 0 and 4, negative 2.5.

Find the x-value where f attains its absolute maximum value on the closed interval from x = -2 to x = 6. Justify your answer. (10 points)

2.

A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10.

What is the velocity of the car when t = 6? You must show your work and include units in your answer.

Linear graph from x equals 0 to x equals 30 with a negative slope. y intercept is y equals 10 and x intercept is x equals 10. (10 points)

3.

Show that f(x) = 2000x4 and g(x) = 200x4 grow at the same rate. (10 points)

4.

A radar gun was used to record the speed of a runner (in meters per second) during selected times in the first 2 seconds of a race. Use a trapezoidal sum with 4 intervals to estimate the distance the runner covered during those 2 seconds. Give a 2 decimal place answer and include units. (10 points)

t 0 0.5 1.2 1.5 2
v(t) 0 4.5 7.8 8.3 9.0

5.












Water flows into a tank according to the rate F of t equals the quotient of t plus 6 and the quantity 1 plus t , and at the same time empties out at the rate E of t equals the quotient of the natural log of the quantity t plus 2 and the quantity t plus 1 , with both F(t) and E(t) measured in gallons per minute. How much water, to the nearest gallon, is in the tank at time t = 10 minutes. You must show your setup but can use your calculator for all evaluations. (10 points)

Quite Quote

QUICK QUOTE

Approximately 250 words

custom essy

Order an essay from experts and get an A+

Address: 679 Dola Mine Road Raleigh
Email: support@academic-research-pro.com
Website: www.academic-research-pro.com
Toll Free: +1800-672-9816

Disclaimer

All Papers produced are meant for reference purposes only. Academic Research Pro does not give the consent and authority to copy and reproduce the papers.

Terms and Conditions | Privacy Policy 

Banner of payment methods of cheap essay writing service