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# Basic Calculus

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### Mathematics - Calculus - Maximum Value

A zookeeper needs to add a rectangular outdoor pen to an animal house with a corner notch, as shown in the figure. If 85 m of new fence is available, what dimensions of the pen will maximize its area? No fence will be used along the walls of the animal house.

### Mathematics - Calculus - Rate measures

A plane flying at an altitude of 25,000 ft. has a defective airspeed indicator. To determine her speed, the pilot sights a fixed point on the ground. At the moment when the angle of depression (From the horziontal) of her line of sight is 65 degrees, she notes that this angle is increasing at 1.5 degrees per second. What is the

### Calculus

A large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point 16.0 m below the water level. If the rate of flow from the leak is 2.50 x 10^ -3 m^3/ min, determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole.

### Mathematics - Calculus - Exponential Functions

A cancer patient undergoing chemotherapy is injected with a particular drug. The function D(h)=4e^-0.35h gives the number of milligrams D of this drug that is in the patient's blood stream h hours after the drug has been administered. How many milligrams of the drug were injected? To the nearest milligram, how much of the drug w

### Mathematics - Calculus - Rate Measure..

A baseball diamond is a square whose sides are 60 ft long. a player running from first to second base has a speed of 25 ft per second. at what rate is the player's distance from home base changing when he is 10 ft from second base?

### Green's Theorem - Work

A particle starts at the point (-2,0), moves along the x-axis to (2,0), and then along the semicircle y= squareroot(4 - x^2) to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x,y)= < x, x^3 + 3xy^2 >.

### Solving Polynomials by factorizing

Factor 1. x^2 + 12x +36 - y^6 2.9y^2 + 12y + 4 - x^2 solve each equation n^2 + n = 72 (4x + 9)(x - 4)(x + 1) = 0 m^3 = m^2 + 12m (x + 4)(5x - 1 ) = 0 x^ + 6x - 7 = 0 A stereo system installer needs to run speaker wire along the two diagonals of a rectangular room whose dimensions are 40 feet by 75

### Mathematics - Calculus - Differential Equation

Please help with this differential equation and an explanation at each step (especially the substitution step) xdx +(y-2x)dy=0.

### Chain Rule and Differential Calculus

Z= x^2 - 3x^2y^3, x= se^t, y= se^-t.

### Minimum Length Problem

A fence 3√3 meters high stands 1 meter away from a wall. What is the shortest ladder that can reach from the fence to the wall? Hint: draw a picture. Let (theta) be the angle the ladder makes with the ground. Part of the ladder goes from the ground to the top of the fence, and the other part goes from the top of the fence to t

### Find all local maxima and minima and all the inflection points

Find all the local maxima and minima and all the inflection points of y = 9x^4 - 11x^3 + 3x^2 + 1. Use the information to sketch Graph of this function, Make it big so everyone can see what is happening (Please see the attached problem.)

### Determine whether the function is a solution of Laplace's equation

See attached file Determine whether each of the following function is a solution of Laplace's equation

### Identify each curve and explain your choices

The figure shows graphs of..... Identify each curve and explain your choices [See attached file]

### Calculus - Functions, Graphs and Derivatives

Calculus - Functions, Graphs and Derivatives (Please see file for complete description)

### Limit -What is the limit of f(x) as x approaches positive and negative infinity where f(x) = (x^3)*e^(-x)?imit -

What is the limit of f(x) as x approaches positive and negative infinity where f(x) = (x^3)*e^(-x)?

### Continuity -State the intervals on which the function is continuous (see attached graph)

State the intervals on which the function is continuous (see attached graph)

### Mathematics - Calculus..

A) Give a possible formula for a cubic function. Assume the graph crosses the x-axis at exactly -3, 1, and 4. Assume it crosses the y-axis at exactly -12. B) The desert temperature, H, oscillates daily between 42ºF at 4am and 82ºF at 4pm. Write a possible formula for H in terms of t, measured in hours from 4am. Give your

### Mathematics - Calculus - Differentiation

Please show detailed steps of how to differentiate the following. .. [See the question file for full description.]

### Mathematics - Calculus - Integrals

Please show detailed steps of how to evaluate the following integrals. Please use natural log. [See the question file for full description]

### Mathematics - Calculus - Derivatives

Find y prime {See Attachment}

### Polynomial functions

Your manager is very pleased with your presentations and being able to show your calculations in a detailed fashion. He has asked that you help him prepare for the upcoming company summit. Before you get together, he has asked that you give him a little review on polynomial functions and how you would apply them to everyday use.

### Graphing the Equation to Find the Lowest Unit Cost

I found that the unit cost of using production equip. is: cost = 1.5x(2)[that is to the 2nd power] - 120x + 4,000 where x is the number of units produced. Draw a graph to find the lowest unit cost. what production level does this correspond to?

### Find the volume of the parallelepiped with adjacent edges

Find the volume of the parallelepiped with adjacent edges PQ, PR, PS P(1,1,1) Q(2,0,3) R(4,1,7) S(3,-1,-2)

### Riemann sum and volume

See attached file Write a Riemann sum and then a definite integral representing the volume of the region, using the slice shown. Evaluate the integral exactly.

### Calculus problem

Please help me in attached problems. A customer ordered a quadratic metal sheet with side length x0=10cm. What is the maximal acceptable error of the side length if the area of the metal sheet should be?... For each of the following functions: state if the function is monotone Decide if it is injective, surjective or bij

### Volume

Pls see attachment, thx

### Basic

Please help with the following problems. See attached. 1. First find a general solution of the differential equation: dy/dx = 3y Then find a particular solution that satisfies the initial condition that y(1) = 4. 2. Given a = <4, -3, -1> and b = <1, 4, 6>, find a x b 3. Use the method of Lagrange multipliers to find

### Mathematics - Calculus Rate Problem

14. A spherical balloon is inflated so that its volume is increasing at the rate of 3 ft^3/min. How fast is the diameter of the balloon increasing when the radius is 1 ft? 16. A 17-ft ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground away from the wall at a constant rate of 5 ft/s, how

### Initial Value - Find the Solution to Initial-Value Problem

Find the solution to initial-value problem: (x^2+1)y'= xe^y with initial condition y(0)= -1.

### You are standing on a hotel balcony 30 feet up from the ground. You want to throw your key to someone standing outside the hotel on the ground ...

You are standing on a hotel balcony 30 feet up from the ground. You want to throw your key to someone standing outside the hotel on the ground. You throw it angled upward with an initial velocity of 55 ft/sec. Assume that the acceleration due to gravity is -32 ft/sec/sec. Find the position function in terms of t. Your frie