Calculus Answers

7. A friend says that finding differentials is as easy as finding derivatives – you just multiply the derivative by dx. Is your friend right?

6. BIOMEDICAL. Weight gain. An average young female in the United States gains weight at the rate of 14(x – 10)^-1/2 pounds per year, where x is her age (10 < x < 19) find the total weight gain from age 11 to 19.

5. ENVIRONMENTAL SCIENCE: Pollution. A factory is discharging pollution into a lake at the rate of r(t) tons per year given below, where t is the number of years that the factory has been in operation. Find the total amount of pollution discharged during the first 3 years of operation.
a. r(t)= t/t^2 + 1
b. r(t)= t square root of t^2 + 16

2. GENERAL: Average Value. The populatin of a city is expected to be P(x)=x(x^2+36)^-1/2 million people after x years. Find the average population between year x=0 and year x=8.

1. Business: Cost. A company's marginal cost function is MC(x)= 1/2X+1 and its fixed cost are 50. Find the cost function.

How do I find the domain of x-x^2/2-3x+x^2?

How can i solve this lim (-1)^n*(n/(n^2+1)) as n->infinity it`s about series. i know that first u have to use the lim-n->infinity | An|. But after that i just get indeterminations forms as 1^infinity.

Find the direction in which the function f x y 2xy 2 2 = − + decreases most rapidly at
the point(1, 1).

2. An ice cube tray filled with tap water is placed in the freezer and the temperature of the water is changing at the rate of -12e^-0.2t degree fahrenheit per hour after t hours. The original temperature of the tap water was 70 degrees.
Questions:
a. Find a formula for the temperature of the water that has been in the freezer for t hours.
b. When will be the ice be ready? (Water freezed at 32 degrees)