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    Basic Calculus

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    Average and Maximum Velocity : Flow of Blood

    The velocity v of blood that flows in a blood vessel with radius R and length l at a distance r from the central axis is v(r)=(P/4(eta)l)(R^2-r^2) where P is the pressure difference between the ends of the vessel and (eta) is the viscosity of the blood. Find the average velocity (with respect to r) over the interval 0 ≤

    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)

    Exchange Rate

    A) Suppose your company has an international operation. Last month, when the exchange rate between the US Dollar and the Japanese Yen was 130.00, your company contracted to purchase inventory from a Japanese company for Y13,000,000, payable in 30 days in Japanese currency. This month the exchange rate is onyl 125.00. Calculate,

    Exchange Rate Gain or Loss

    A) Suppose your company has an international operation. Last month, when the exchange rate between the US Dollar and Japanese Yen was 130.00, your compnay contracted to purchase inventory from a Japanese company for Y 13,000,000 payable in 30 days in Japanese currency. This month the exchange rate is only 125.00. Calcualte, if a

    Related Rates Found

    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?

    Business Calculus : Rate of Change, Slope of Tangent

    1. Consider the following table: X 0 1 2 3 4 5 Y 1.5 2.4 3.6 4.5 5.6 6.7 For each of the following intervals, find the average rate of change: (a) [0,1] (b) [0,3] (c) [2,5] (d) [0,5] 2. Consider the following table: X 1 2 3 4 5 6 Y 24 26 28 27 25 23 For each of the following intervals, find the average rat

    Usub and parts

    Please give step by step detailed solutions and answers to all. Please oh please do not skip steps. I need to see all these problems done so I can understand them and the way to think of solving them. I cannot find a one on one tutor and since I am auditing this course just for knowledge the teacher does not want to waste the

    Usubstitution and integretion by parts

    Please give step by step detailed solutions and answers to all. Please oh please do not skip steps. I need to see all these problems done so I can understand them and the way to think of solving them. I cannot find a one on one tutor and since I am auditing this course just for knowledge the teacher does not want to waste the

    Mean Value Theorem and Intervals

    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)

    describes several types of math software.

    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 bo

    Analyticity Disk Function

    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 Investigated

    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

    Isolated Singularities of Functions

    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*

    Exact Value for Difference Identities

    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 -√2/2 √2/2 √3/2

    Calculus and Analysis: Temperatures

    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 Example Problem

    A particle is moving along the curve y=sqrt x. As the particle passes through the point (4,2), its x-coordinate increases at a rate of 3 cm/s. How fast is the distance from the particle to the origin changing at this instant?

    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 Example

    A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking?

    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?

    Related Rates and Differential Equations

    (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt. (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius

    Finding Average Velocity & Instantaneous Velocity

    If a ball is thrown into the air with a velocity of 40ft/s, its height in feet after "t" seconds is given by y = 40t-16t^2. a) Find the average velocity for the time period beginning when t=2 and lasting (i) 0.5 seconds (ii) 0.1 second (iii) 0.05 seconds (iv) 0.01 second b) Find the instantaneous velocity when t=2.