Find a polar equation in the form r = f(8) of the hyperbola with eccentricity e = 4 such that one of its foci is the pole and the nearest vertex to the pole has polar coordinates (2, 0)

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Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

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Q: 5. Graph the linear inequality on the graph. x<-4

A: Given data÷

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A: Let's find. 

Q: Use the guidelines of this section to sketch the curve. х — 5 f(x) x2

A: f(x)=x-5x2Plotting on graph on corrdinate axes

Q: Find the requested partial derivative. dz 3 if z° = z+ xy - 1 and y = x+ y- 1 dy 3

A: We have to find partial derivative 

Q: Sketch the region bounded by the given curves, then find its area. y = x^2, y = 2x

A: Given,            The equation of the curves are y=x2 and y=2x.To find : Find its area.

Q: a) Determine the second derivative of the following i) g(x) = - ii) h(x) = Vx³ + x – 1 %3D

A: We have to find the derivative of the given functions.   According to our guidelines we can solve on...

Q: 5. x = 8 – y², x = y² – 8

A: This question is based on application of definite integral.

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Q: Find the tangent line approximation T to the graph of f at the given point. Then complete the table....

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Q: Consider the function f(x) = 2x3 – 6æ² – 48x + 3 on the interval [-5, 8]. Find the average or mean s...

A: mean value theorem

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Q: Which of the following functions are solutions of the differential equation y" + y = 9 sin(x)? y = 9...

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Q: Choose a correct statement concerning the function f(x, y) = 3x² – e2y. O There are local minima but...

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Q: The plane that contains the point (3, –1, -4) and the line with equation y – 1= 3z is orthogonal to ...

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Q: The length l, width w, and height h of a box change with time. At a certain instant the dimentions a...

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Q: 2. Solve 3shn-sinx-2= over the interval [0,27). 2 sın'x-sinx-|:0

A: The objective is to solve the above expression.

Q: dy -2 sin x where y (5 = JT dx

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Q: Estimate the slope of the tangent line at the point t = -7, for f(t) = 15t – 1. (Give your answer as...

A: Slope of tangent line

Q: 9. If 8000 dollars is invested in a bank account at an interest rate of 6 per cent per year, compoun...

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Q: Find the derivative of the function at Po in the direction of A. f(x,y) = - 4xy + 3y², Po(4, - 2), A...

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Q: 2. If y = xlnx,

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Q: 36,37

A: As per our guideline is multiple questions are posted we are supposed to answer only the first one. ...

Q: n 1.3.5. ...· (2n – 1) 5nn! n=1

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Q: 3. y = 12 – 3x, y= 4 – x2

A: Given query is to find the area bounded by the curves.

Q: 3x°- 4x g(x) = 2 x' +2 Find the derivatives final should have no negative powers. answer

A: We have to determine above derivative 

Q: 3. Given the equation y = In(cos(x)): What is dx/dy? secx -seox -tanx -cotx None of the choices.

A: I am attaching image so that you understand each and every step.

Q: Find the area of the region under the graph of f(x)=2x2−4x+2 on [−2,3].

A: The area can be calculated using the concept of definite integral.

Q: Evaluate the following integral over the Region D. (Answer accurate to 2 decimal places). I 5( . sin...

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Q: For the function f(x) = 3x* - 2x -2x +7, find f"(x). Then find f"(0) and f'"(6). %3D E"(x) =D Select...

A: We can answer the questions as below.

Q: Sketch the region bounded by the given curves, then find its area. x=y2, x=y+6

A: Here we have to sketch the region bounded by the given curves.  We have, x=y2, x=y+6

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (cos(0), sin(0), –1) v= (sin(0),...

A: The objective is to determine whether U and V are orthogonal, parallel or neither. 

Q: Let D be the trapezoidal region in the ry-plane bounded by the graphs of z = 0, y = 1, y = z and y =...

A: We have to solve for the area by integration. 

Q: The graph of a function y = f(x) is shown. At which point(s) are the following statements true? (Sel...

A:     f'(x)=0 at A' and D.At A, f'(x)&lt;0, f''(x)&gt;0At B, f'(x)&gt;0, f''(x)&gt;0At C, f'(x)&gt;0,...

Q: the curve C:r = 1+ sin e and above the line e: r= 3/4 c

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Q: A street light is at the top of a 13 ft tall pole. A woman 6 ft tall walks away from the pole with a...

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Q: Graph the function, considering the domain, critical points, symmetry, regions where the function is...

A: topic - sketch of a function

Q: 15. f(x) = for every x E (-4,3] x+4 16. f(x) = sin (2) in the interval x 2-2 3 17. f(x) = { 2 - x2 i...

A: As per our guide lines we are advised to solve only first question. Please kindly upload other quest...

Q: aie of sin(4x)+8 cos(x)+2x2 cos(4x)+8x sin(4x)+.

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Q: 1. Let f (x) = x (cos(2a)+ sin(3x)). a. Find the average value of f (x) for 0 <x < T. Show your work...

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Q: WWhe cycloid SO of arch of the cycloidis genorated as t varies from

A: To find the area.under the arch

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Q: 10 respective An accessories company finds that the cost and revenue, in dollars, of producing x bel...

A: Given query is to rate of change of average profit.

Q: 1. Approximate the area under the curve of y = e¯** from x = 0 to x = 1 using: a. R4 h Le %3D

A: Reimann sum

Q: Evaluate the following indefinite integral (sin z)(tan z) dr. cos I

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Q: Show that the function f(x) = |x - 2| is not differentiable at 2. We have if x 2 2 f(x) = |x - 21 = ...

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Q: Calculus

A: Topic:- calculus

Q: A cylinder shaped can needs to be constructed to hold 250 cubic centimeters of soup. The material fo...

A: Find out the dimensions that will minimize the production cost.