10 Short Answer Calculus

Question Description

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)

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)

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 with y(0) = 4 does not have a solution.

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

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)

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)

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)

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

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

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)



^{Have a similar assignment? "Place an order for your assignment and have exceptional work written by our team of experts, guaranteeing you A results."}

Our Service Charter

1. Professional & Expert Writers: Eminence Papers only hires the best. Our writers are specially selected and recruited, after which they undergo further training to perfect their skills for specialization purposes. Moreover, our writers are holders of masters and Ph.D. degrees. They have impressive academic records, besides being native English speakers.

2. Top Quality Papers: Our customers are always guaranteed of papers that exceed their expectations. All our writers have +5 years of experience. This implies that all papers are written by individuals who are experts in their fields. In addition, the quality team reviews all the papers before sending them to the customers.

3. Plagiarism-Free Papers: All papers provided by Eminence Papers are written from scratch. Appropriate referencing and citation of key information are followed. Plagiarism checkers are used by the Quality assurance team and our editors just to double-check that there are no instances of plagiarism.

4. Timely Delivery: Time wasted is equivalent to a failed dedication and commitment. Eminence Papers are known for the timely delivery of any pending customer orders. Customers are well informed of the progress of their papers to ensure they keep track of what the writer is providing before the final draft is sent for grading.

5. Affordable Prices: Our prices are fairly structured to fit in all groups. Any customer willing to place their assignments with us can do so at very affordable prices. In addition, our customers enjoy regular discounts and bonuses.

6. 24/7 Customer Support: At Eminence Papers, we have put in place a team of experts who answer all customer inquiries promptly. The best part is the ever-availability of the team. Customers can make inquiries anytime.