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# Derivatives

### Trapezoidal Rule

Let L(x) = int(1/t, t=1..x) for all x>0. a) Find L(1). b) Find L'(x) and L'(1). c) Use the Trapezoidal Rule to approximate the value of x (to three decimal places) for which L(x) = 1. d) Prove that L(x1 * x2) = L(x1) + L(x2), for x1 > 0 and x2 > 0. [Obs: My CAS is Maple]

### Differential calculus proof

See attached. The (n-1)-dimensional sphere can be realized as the zero set of the function.....

### Derivatives and Tangents

Please see attachment. Find the derivatives of the functions...

### Find the Derivatives of Functions

Please see attachment Find the derivatives of the given functions... Find the equations of all lines through the origin tangent to the parabola...

### first derivative and second derivative

Please see the attached file (word problems, inflection, critical points, and derivatives) 14. You run a small furniture business. You sign a deal with a customer to deliver up to 400 chairs, the exact number to be determined by the customer later. The price will be \$90 per chair up to 300 chairs, and above 300, the price wil

### Drawing a Function: Example Problem

1. Draw in a surrounding of O the graph of the following function: f(x) = -1 + 3x - (3x)2 + (3x)3 - (3x)4 + ........ showing the value in O of the derivative first, second, and tenth. (See attached)

### Application of Derivatives of Function

(See full description in the attachment). 1. With a yearly rate of 3 percent, prices are described as P = P0 (1.03)^t, where P0 is the price in dollars when t = 0 and t is time in years. If P0 is 1.2, how fast are prices rising when t = 15? 2. The value of a car is falling 10 percent per year so that if C0 is the purchase p

### Drag and Velocity

See attached for problems.

### Differentiation and Radius of Curvature

See attached for formulas

### Differentiation proof

See attached. In this question, p denotes dy/dx. Given that y=p^2+xp, show by differentiating with respect to x that dx/dp=-2-2x/p....

### Find the Partial Differentiation

Find the partial derivative. [See the attached question file.]

### Managerial Finance - Ratio Analysis for Walmart and Target

Hello, Please assist me with the following study for my exam. Evaluate each firm's financial performance for the two most recent years available by (1) performing financial ratio analysis using the MicrosoftÂ® ExcelÂ® Ratio Analysis Worksheet, (2) performing trend analysis on those financial ratios. Your analysis should in

### Rules of exponential function

Please see the attached file for full description. Post a response to the following: Explain three rules for exponents listed in the chart on p.239 (section 4.2). Do not explain the first two definitions listed in the table (Exponent of 1 or 0). Create an expression for your classmates to solve that uses scientific notation a

### Differentiation and critical points

1.) Differentiate these functions. a.) (sqrt(x)+1)/(x^2) b.) 3^x (cubedroot of (x+5)) - ((ln(x))/sqrt(x)) ----------- 2.) Consider the function f(x)= x^3- (1/2)x^2 - 4x + 5 a.) find all critical points of 'f '. b.) Does 'f ' have an inflection point? Explain your answer. c.) Determine the intervals on which 'f '

### Derivative Setting Values

Please check the following derivative and explain how setting it equal to 0 you can get the value for r.

### Find the Max and Min. values attained by the function

I need the following problems worked out in Microsoft Word with equation editor. See the attached file. Thank you, Problem 1- Fig. 1.1 Find the Max and Min. values attained by the function (fig 1.1) on the interval [0,2] Problem 2- Fig. 2.1 A mass of clay with a volume (fig. 8.1) is formed into two cubes. W

### Using the graph of a function to graph the derivative of that function.

I have attached a graph that is the first derivative of a function. How do I find and draw the second derivative on this graph? I am unsure of how to do this without a given function.

### Velocity and acceleration

The graph of the velocity v(t), in ft/sec, of a car traveling on a straight road, for 0 is greater than or equal to t is greater than or equal to 50, is shown in the attachment. A table of values for v(t), at 5 second intervals of time t, is also in the attachment. a.) During what intervals of time is the acceleration of the

### Partial Derivatives - See attached file for the problem.

See attached file for the problem.

### Finding Directional Derivatives

Consider the function f(x,y,z)= e^xy cos(x+z). What is the directional derivative for f at the point P(0, -pie/6, pie/3) in the direction u parallel to i - j + 2k

### With a yearly rate of 3 percent, prices are described as

1)With a yearly rate of 3 percent, prices are described as P = P0 (1.03)t, where P0 is the price in dollars when t = 0 and t is time in years. If P0 is 1.2, how fast are prices rising when t = 15? 2)The value of a car is falling 10 percent per year so that if C0 is the purchase price of the car in dollars, its value after t

### Derivatives - Product, Chain Rules, Application type

Differentiate the following problems. Assume A, B and C are constant. Show all work. f(x)=2ex+x2 P=3t3+2et y=5*2x-5x+4 P(t)=12.41(0.94)t y=10x+10/x y=t2 + 5 ln t y=x2 + 4x - 3 ln x Solve the following problem and show work For the cost of function C = 1000 + 300 ln q (in dollars) find the cost and the

### Simple Problems on Derivatives

Questions are in the attached file.

### Derivatives: Temperature of a Reaction

The temperature of a chemical reaction is given by the formula: T(t) = 8e-0.3(t-2)^2 + 7, where T is the temperature and t is the time in seconds since the reaction was started. a) Draw a neat graph showing the reaction temperature during the first eight seconds of the reaction. b) What is the maximum temperature reached dur

### Derivatives - A High School Principal

The complete question is in the attached file.

### Rate of Change/Derivative: Car Loan

Suppose C(r) is the total cost of paying off a car loan borrowed at an annual rate or r%. What are the units of C'(r)?

### Derivatives and Asymptotes

Please see the attached file for full problem description. 1. Does the graph of a function have a horizontal asymptote? If the answer is positive, find the equation of the asymptote 2. Find , when 3. Find the derivative of 4. Find the derivative of using the definition of the derivative 5. Find the antid

### Find the derivative of the function.

See the attached file. Find the derivative of the function. Find the derivative of the function. f(x) = (2 - e-6x)9 Find the derivative of the function. f(s) = (s9 + 1)e-s9 Find the derivative of the function.

### Derivatives

Please see the attached file. Use the following equation to find &#8706;z/&#8706;x and &#8706;z/&#8706;y.