a) Convert the point whose polar coordinates are (4, 5pi/4) to rectangular coordinates.

Q: 3. Sketch these functions and find their domain and range. a) f(x) = √√3x b) y = x³

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Q: Using the graph of f'(x) find the increasing/decreasing intervals of f, points on  axis which f has…

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Q: Determine the value of the definite integral that describes the shaded region above. 1. 9dw

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Q: 6. Σ. 1 n=1 1 ηγη2 +1 n

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= 8 cos 0+6…

A:

Q: 4. Solve Cauchy problem: y" - 5y' + 4y = 0, y(0) = 1, y'(0) = 2

A: To solve the following Cauchy problem.

Q: Given the ellipse : 1 (x+2)² + (−1)² = 9 4 (a) Graph the ellipse, together with its major and minor…

A: The blue dashed line represents the horizontal and vertical lines passing through the center.

Q: 2 0 0 1 -2 1 0 4 -3

A: given matrix is ,

Q: derivative xy = e -xy

A:

Q: 19. What is the maximum volume of cylindrical tin can that can be made from 750.0 cm² of metal?

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Q: et P(x, y) denote the point where the terminal side of angle 8 (in standard position) meets the unit…

A: The figure

Q: 5. 6% a. x-2 dx 1-sin 2x 2 x-sin-x dx 2 + tan² x x + tan x - dx

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Q: Find the domain of f(x). f(x)=√x² + 7x + 10

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Q: Find the slope of the tangent line to the graph of the polar equation at the point specified by the…

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Q: Let g(t) = - 503 t Determine the most general indefinite integral of g. - 5 + dt

A: Given,

Q: Find the average value of the function g(t) = 1 + t over the interval [0, 4].

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Q: 2 5. Represent the function as a power series f(x) = o Cnx". Compute the first few 1-7x coefficients…

A: The function 2/(1-7x)

Q: 3. Use the definition of Taylor series to find the Taylor series centered at a = 1 for f(x) = ln x

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Q: Find an equation in rectangular coordinates for the spherical equation p = 4 sec (6)

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Q: 6. Find the sum of the series: 100 x5n−1 n!

A:

Q: y=3in (2+x²)

A: y=3ln⁡(x2+2)dydx=ddx{3ln⁡(x2+2)}ddxln⁡x=1xChain Ruleddxf(g(x))=f′(g(x))g′(x)dydx=3x2+2ddx(x2+2)

Q: S 12x+8 3x²+4x+8 dx

A:

Q: Determine the amplitude, period, and phase shift for the given function. - cos(2x - 5) y=1- 1…

A: To determine the amplitude, period, and phase shift for the given function.

Q: The original 24 m edge length x of a cube decreases at the rate of 3 m/min. a. When x = 6 m, at what…

A:

Q: Suppose g is a function which has continuous derivatives, and that g(0) and g"" (0) = 18. What is…

A: Suppose  is a function with continuous derivatives, and that .To find the Taylor polynomial of…

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: To find a formula for the general term  of the following sequence.

Q: height (feet) of an object moving vertically is given by s= - 16t² +288t+216, where t is in seconds.…

A:

Q: √(x ³ ex² + 4x + ex¹ +4x) dx.

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 16. Split the number 15 into two parts so that the product of one part and the other is maximized.

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Q: (d) lim Bl x-l lnx (e) lim x-x)

A:

Q: Find the derivative of the function. y = 7x-6 8x+3

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Q: ← The following graph shows the rate of inhalation of oxygen (in liters per minutes) by a person…

A: From the given data and graph,we can useLeft Riemann sumeach width= h =1At x=1, f(x)= 2.7 At x=2,…

Q: 3. Two savings account start with $100 each. Account A earns $2 annually while account B earns 2%…

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Q: The area of a circle increases at a rate of 4 cm^2/s.   Part A How fast is the radius changing when…

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Q: 224. Suppose that a particle moves along a straight line with velocity defined by v (t) = t² – 3t –…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi +…

A: We have to find the flux of the curl of the field F using surface integral in Stoke's Theorem.Given…

Q: Find the areas of the shaded regions in

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Q: problem finds the derivative of a function at a point using the formal definition. The process is…

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Q: Perform the following operations and simplify the results. State the domain restriction in each…

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Q: se the given information to evaluate each expression. (Enter your answers in exact form.) sin a =…

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Q: In the following exercises, use a change of variables to evaluate the definite integral. 2 294. ² t…

A: By changing the variables, to evaluate the following definite integral.

Q: 1. For the function g(x) graphed here, find the following limits or explain why they do not exist.…

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Q: Find the cost function for the marginal cost function. 7 C'(x)=9x; 10 units cost $171.99 X Write the…

A:

Q: 4x Suppose that Σε (9+ x) n=0 Find the first few coefficients. =

A: 4x(9+x)=∑n=0∞cnxnWe know that the Mclaurin series of 11+x11+x=∑n=0∞(−1)nxn

Q: 1. Ση=1_n3 +1° η n?

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: The average household received 24 pieces of mail each week. The number of bills and statements is…

A: The average household received 24 pieces of mail each week. The number of bills and statements is…

Q: √ 5x(x² +4)√√x² + 4 dx. 2

A: To evaluate the following integral.

Q: For what value of a is the following function continuous at every x? f(x) = x²-30, x<10 x≥ 10 ax,…

A:

Q: List the first five terms of the sequence. a1 = 5, 2n + 1 2an +4 а1 а2 аз ад a5

A: To list the first five terms of the following sequence.

Q: 1 Assume that f'(4) = -5, g'(2), g(2)=4, and y=f(g(x)). What is y' at x = 2? 8 Atx=2, y'= (Simplify…

A: The chain rule of differentiation is given by