A rectangle is constructed with its base on the diameter of a semicircle with radius 16 and with its two other vertices on the semicircle. What are the dimensions of the rectangle with maximum area?

Q: dx If the derivative dy (instead of 2) exists at a point and = 0, then the tangent line at that…

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Q: 53. If sin (t) = -! and t is in the 3rd quadrant find cos(t)

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Q: 1 Determine by the direct comparison test if Ln=1 2n+1 converges or diverges .

A: We have to find convergence test

Q: 4. Find 2+1dt O V4x+1 O V16x? +1+v2 O 4/16x? +1 O V16x? +1

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: Find the exact area of the surface generated when the curve f (x) = /5 – x on the interval 3 <x < 5…

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Q: Find polar coordinates to represent (-2, -2) with r >0 and 0 <0< 2T.

A: Cartesian to polar conversion (x,y)→(r,θ) where r=x2+y2 θ=tan-1yx

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Q: dA when T = 5. dt dr Let A be the area of a circle with radius r. If dt 2, find %3D

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Q: An open box is to be made by cutting small squares from the corners of rectangular board and then…

A: let "x" be the length of the side of the square cut.Length= 8-2xWidth = 6-2xHeight =xVolume =…

Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 24 cm to a length…

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Q: f(Tn) for For the function f(x) = tan(r), write Newton's formula as Tn+1 = F(xn) = In [(").f solving…

A: Find your answer below

Q: 5 (b). ( the base radius making the surface area minimum. ) Consider a cylinder having fixed volume.…

A: Use the application of derivative to minimise the surface area.

Q: 2) Find the sum of the first 100 terms of the arithmetic sequence: 2, 4, 6, 8, 10, 12, ...

A: The arithmetic sequence: 2,4,6,8,10,12,.......

Q: Express the Cartesian coordinates (-3,1) in polar coordinates in at least two different ways. Write…

A: We have to convert in polar coordinates.

Q: The volume of the solid obtained by rotating the region enclosed by y = x², x = 2, x= 3, y=0 about…

A: We have to find the volume of the solid.

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: Let's find.

Q: 72-1 b) En=1an for an 5. )** 00 %3D

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Q: Calculate Ls for on the interval

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Q: Describe the given region in polar form a.) b.), 1 1 2/3

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. 9 y dy 6 У - 2у - 3…

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Q: | 13t – 41° + 4 dt = +C.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: he volume, V, of a sphere in terms of its radius, r, is given by V (r) = Tr3. Express r as a…

A: Topic:- function

Q: answer

A: We will find the particular solution.

Q: yA C(0, 1) B(1, 1) y=Vx R2 R3 R1 A(1, 0) Referring to the figure above, find the volume generated by…

A: This question can be solved using the concept of volume of solids generated as a result of rotation…

Q: dy The curve with equation y= has a stationary point in the interval -1 <x < 1. Find and 1-x dx…

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Q: Use the power series Σ 2(-1)^x^, \x| < 1 1 + x n = 0 to find a power series for the function,…

A: Leibnitz Alternating series Test :  Suppose that we have a series ∑(-1)n an where , an≥0 . Then if,…

Q: Write the sum using sigma notation: 9+ 13 + 17 + 21 + ...+ 57 = B, where n=1 A = B =

A: Topic:- sequence and series

Q: Use the table of frequently used Taylor series to find the sum of the series. - 3+ 6x - 9x + 12x -…

A: Solution

Q: a a If f is an even function, why is f(x) dx = 2 f(x) dx? Choose the correct answer below. O A. a a…

A: Definite integration property

Q: dr J. (z+1)?

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Q: If the change of variables u = x -2 is used to evaluate the definite integral f(x) dx, what are the…

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Q: Solution :- we have Fla) =5 cas 2x %3D Now di'fferentiate it wot x x d (cos2x) %3D Źx(-2sin2x) %3D…

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Q: Use the Root Test to determine whether the series convergent or divergent. n2 + 7 \" 9n2 + 5 00 n =…

A: We have to find out the series convergence test

Q: If f(x) = [(1³ + 6r² + 1) dt

A: Here, the given function is: f(x)=∫0xt3+6t2+1dt...(1) Note that, the Fundamental Theorem of Calculus…

Q: Use geometry to find the displacement of an object moving along a line for the time intervals…

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Q: Find an equation of the plane through (-7, 2, 1) that is 2 = 3t, y +3 = 6t, z = perpendicular to the…

A: We know that equation of plane passing through the point (x1,y1,z1) and normal n=ai+bj+ck is…

Q: A tank is full of water. Find the work (in ft-lb) required to pump the water out of the spout. Use…

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Q: a lim - o Consider the following series. * (-1)* * 1 (jerror 0, and then you need to verify the two…

A: Given: Here, bn+1=(-1)n+1+1n+17=1n+17. We are given the bound ε=0.00005. So, now we need to solve…

Q: Dr. Barrett wants to purchase a new piece of equipment for his practice. The eauipment can be…

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Q: Evaluate the sum. Σ (-2) k 2 k=2

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Q: Find the length of the curve y ' = 8x from x=1 to x = 8 www

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Q: onvert (-1, v3

A: Given point (-1, 3)

Q: Webkasign. Graphing Tool Solve the system. (f there is no solution, enter NO SOLUTION. I the system…

A: we have to find solutions

Q: of and dy of For the function f(x,y) = In (9x + 8y), find

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: Find the limit. (If an answer does not exist, enter DNE.) lim (x + Ax)² – 4(x + Ax) + 9 – (x² – 4x +…

A: In this question we can find limit.

Q: Find the equation of the tangent line to the curve y = e' when it is paralel to 2r-y =7.

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