# Calculus Homework Assignment

*label*Mathematics

*timer*Asked: Feb 9th, 2019

*account_balance_wallet*$9.99

### Question Description

There is a total of 9 questions that I need help with. 4 that I partially answered and 5 that I need help with understanding how to complete the problem. One has to do with finding the equation of a tangent line, one has to do with l'Hospital's rule, one has to do with approximating cost, one has to do with velocity, and multiple have to do with marginal cost/profit/revenue. If you need more time to given me explainations that's okay, I just need the answer within the time limit.

### Unformatted Attachment Preview

## Tutor Answer

Attached are the solutions. Please let me know if you have any questions or if there are any errors.

Start by finding the derivative of the function:

f(x) = 5x^-2

f'(x) = 5*-2x^-3 = -10/x^3

Evaluate the function and the derivative at the point x = 1

f(1) = 5/1^2 = 5

f'(1) = -10/1^3 = -10

f'(1) will be the slope of the tangent line.

Use point slope form to develop the equation for the tangent line

y – y1 = m(x – x1)

y – 5 = -10(x-1)

y -5 = -10x + 10

y = -10x + 15

Evaluating at negative infinity would give you a indeterminate form. Take the derivative of the

top and bottom by applying l'hopitals

lim(x--> - inf) 14x + 10 / 12x – 5

Evaluating this limit at negative infinity would still give you in indeterminate form of – infinity / infinity. That means you should apply l'hopitals rule one more time

lim(x--> -inf) 14 / 12 = 14/12 = 7/6

The limit is 7/6

P'(4) was equal to 35. If t = 4, that means the year would be 2000 + 4 = 2004.

The rate would be 35000. Remember P is in thousands of dollars, so 35 really means 35000

Box 1: 35000

Box 2: 2004

Start with s(t) and set that equal to zero. That will tell you the time when the rock reaches the

ground

0 = 400 – 16t^2

16t^2 = 400

t^2 = 25

t=+-5

Since you cannot use a negative time, you should focus on the t = 5

Now you also needs to find the velocity at that time by plugging t = 5 into your derivative

equation.

S'(5) = -32*5 = -160 ft / sec

Box 1: - 160

Box 2: 5

The revenue function can be fo...

*flag*Report DMCA

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors