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Basic Calculus

Calculus: Four good word problems in calculus

#1 A tumor may be regarded as a population of multiplying cells. It is found empirically that the "Birth Rate" of the cells in the tumor decrease exponentially with time, so that B(t)=B0e^(-at)... find the limiting population of the tumor. (See attachment for full questions)

Related Rates

Let z = x^2 + y^2, where x and y are increasing at the constant rates of 2 units per second and 3 units per second, respectively. What is the set of points for which the rate of change of z is zero?


Use the Mean Value Theorem to find c = _________________ the value, or values, of c for the following function, in the interval [- 1, 1], that satisfies the theorem. For x>=0, G(x) = 1 + x^2 For x < 0, G(x) = 1 - x^2

Mean Value Theorem

Use the mean value theorem to find c = _______ The value(s) of c for the following function, in the interval [1,e], that satisfies the theorem f(x) = ln(x)

Software question

I am looking for a software package that can solve simple random equations like f(x,y) as an "input" and plot the 3-D results as the "output" using x, y and jx. My object is to view both real and imaginary parts of the graph on one x, y and jx 3-D coordinate system while using y as the independent variable. Complex math softwa

Force, direction, velocity

To go from one city to another a plane must fly 1756 km at an angle of 71 degrees south of east. How far south and east is the second city from the first? A boat heads directly across the river with a velocity of 27 km/h. The current parallel with the bank is at 14 km/h. What are the resulting direction and velocity of the

Analyticity question

Suppose f is analytic on the disk |z|<1 and that f(0)=0. Let g(z)=f(z)/z. Then g is analytic on the region 0<|z|<1. How can you define g(0) to make g an analytic function on all of |z|<1? Briefly explain why the choice makes g analytic at 0.

Riemann Sum

Q. Show directly that the function {see attachment}, is integrable on R = [0,1] x [0,1] and find {see attachment} (Hint: Partition R into {see attachment} squares and let N ... {see attachment})

Minimum possible width

A long rectangular sheet of metal strip is to be made into a rain gutter by turning up two sisdes at right angles to the remaining center strip. The rectangular cross-section of the gutter is to have an area of 18 in^2. Find the minimum possible width of the strip. Could you please show all work so I can better grasp the co

Classifying Isolated Singularities

Classify all the isolated singularities of the following functions (classify as removable, pole of order m, or essential). Explain the reasoning for each classification. *See attachment for functions*


Find the exact value by using a sum or difference identity. Which is the correct answer? cos 20 cos 25 - sin 20 sin 25 (angles are in degrees) 1 -&#8730;2/2 &#8730;2/2 &#8730;3/2

Calculus and Analysis

Celsius and Fahrenheit temperatures, C and F, are related by a linear equation of the form C= m F + b, and its graph is a straight line in the (F,C), plane that passes through two known points (F,C) = (32,0) and (212,100) for the standard freezing and boiling points of water, respectively. Find the equation of the above line giv

Related rates

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s. (a) At what rate is his distance from second base decreasing when he is halfway to first base? (b) At what rate is his distance from third base increasing at the same moment?

Related rates

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?


Before starting, the answer to the 2nd problem is NOT y=3.9x+20 or y=4.1x-300. Those are the solutions to the first part of the question. The second part is asking for the TOTAL cost when you have "x" amount of feet, not just the cost of digging ONE foot. I posted earlier and received the above answers. The question I would like

Tunnel Problem

In the summer of 1999, construction will begin on a 3000 ft. tunnel that will pass under the Mississippi River, connecting the cities of East St. Louis, Illinois and St. Louis, Missouri. A Missouri-based company has been contracted to begin excavating the tunnel from the Missouri side, while an Illinois-based company will begin

Integer Linear Regression

ASW Publishing Inc., a small publisher of textbooks, must make a decision regarding which books to publish next year. The books under consideration are listed in the following table, along with the projected three year sales expected from each book: Book Subject Type of Book Projected Sales (1000's) Business Calculus Ne

Rate of Flow

A fluid has a density 1500 and velocity field of: v = -yi + xj + 2z k. Find the rate of flow outward through the sphere x^2 + y^2 + z^2 = 25.


30) If f(x) = ln(sin(x^2)), then f''(x)=? Explain. 31) The college is making parking lot, rectangular and enclose 6000 sq meters. A fence will surround the lot and on parallel to one of the sides will divide the lot into two sections. What are the dimensions in meters of the rectangle lot using the least amount of fen