Find the exact length of the polar curve. r= theta, 0<= theta <= 3(pi)/4

Q: Which of the following is continuous at all points? x²-4x-5 x2+2x-35 A) f(x) = B) f(x) = x-5 x-5…

A: Note : “Since you have posted multiple questions with multiple sub-parts, we will solve first…

Q: Consider the equation below. = 9 cos2(x) – 18 sin(x), 0 < x < 2n (a) Find the interval on which f is…

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Q: Solve the equation. Write the solution set with the exact values given in terms of common or natural…

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Q: Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.…

A: Formula used:logan=nlogalogab=log(a)-log(b)loga.b=log(a)+log(b)

Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. 00 17 Σ…

A: Given query is to find series converges or diverges.

Q: Write  z1 and z2  in polar form. z1 = 7 + 7i,  z2 = 16

A: We need to convert the complex numbers into polar form.

Q: If m s f(x) s M for a s x s b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: Solve: y" + 9y = 9csc3x O y = C1 cos3x + C2 sin3x – 3xcos3x + sin3xln(sin3x)

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Q: Find the absolute maximum and minimum values of f(x) = -(x² + x) interval [-3, 4]. over the absolute…

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Q: 4. Express the following single logarithm: as a i) log3 54 -log3 6 ii) 2 In (5a’b) – In (125 aº b²)…

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Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: 78 |x cos(nx)dx

A: As per guidelines we will solve one question

Q: The restaurant at the top of the Space Needle in Seattle, Washington, is circular and has a radius…

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Q: Find the angle 0 shown in the right triangle below. 10 Give your answer in radians and rounded to…

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Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y= 11 x,…

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Q: A -r = COs(U) TC Ex: Replace P(r, 0) → P(x, y) and graph. rcos (0-) = 3. (H.W %3D

A: The given equation is: rcosθ-π3=3

Q: Find the critical numbers of the function. x – 1 | f(x) : x² + 4

A: find the critical points of the function f(x)=x-1x2+4

Q: 7 p(x) = iven the expression Vy7 – 2 this mathematical expression stated correctly.

A: Given query is to find expression is correct or not.

Q: Must the values be ordered from smallest to largest for the method to findNewton polynomials to…

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Q: The volume of the solid under the plane 3 x+ 3 y -z=0 and above the region enclosed 23 by y=2 x and…

A: y=2x and y=2x22x=2x2x2-x=0x(x-1)=0x=0, y=0x=1, y=2

Q: p*² /2 Cos /2.rdx

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Q: | 2f(x) + ldx

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Q: Having been asked to design a brass plumb bob that will weigh in the neighborhood of 180 g, you…

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Q: Sketch both parametric curves below. Then determine if they intersect. If ney intersect, find the…

A: To solve the following problem

Q: 1. f o¬* xy dy dx О а. 32/3 O Б. 16/2 Ос. 32/4 O d. 18/4

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Q: 25) Show that the curve with parametric equations x = tcos(t) , y = tsin(t), lz = t ies on the cone…

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Q: a cost function of C=16x2−133x+9878C=16x2-133x+9878, where CC is the cost in dollars and xx is the…

A: Given query is to find the units to minimize the cost.

Q: Solve the equation. Write the solution set with the exact values given in terms of common or natural…

A: Given, 107+6r +7500= 121000 Simplifying the above equation we have, 107+6r = 113500

Q: Consider the following. (If an answer does not exist, enter DNE.) F(x) = x/6 – x (a) Find the…

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

Q: x 4 kx + 3, а. Let g(x) = 8, a) Find the value of k if g (x) is continuous at x 3. b) Determine…

A: Solving

Q: 3– 2n For s,= determine the convergence or divergence of the sequence (sn). Find any 7. 1+n limits…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the change in cost C for the given marginal. Assume that the number of units x increases by 3…

A: We have to find the change in cost C.

Q: V9 - 4x? dx

A: See the details solution in below

Q: A small metal bar, whose initial temperature was 20° C, is dropped into a large container of boiling…

A: Newton law of cooling : dT/dt = k(T - Ta) and T = Cekt + Ta Boiling Temperature of water is 100° C…

Q: 2. Find the work done by F in moving a particle once counterclockwise around the given curve C F =…

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Q: Given the equation y = 5 In| 6y | Find the Implicit derivative " dy/dx" of the function. You will…

A: We can find the derivative as below.

Q: 2 4 dpx. (px)2 ACS = 1

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Q: Evaluate the definite integral. t1/3 t2/3) dt 3 20

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Q: 4-ス しx-x2 しim

A: limx→164-x16x-x2Apply L-Hospital

Q: Find the nth term of a sequence whose first several terms are given. 2, 5/4, 8/9, 11/16, 14/25

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Q: Find the tangent lines as directed. To the ellipse x²+2y²=9 perpendicular to the line 4x-y=6

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Q: | sin rdr 3.

A: Here we have to solve the given integration by using integration by parts.

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. (Enter…

A: The given equation is: 5x2=61-x   As we know that; logaxb=b·logax ; x≥0

Q: b. f(x) = xe-*, g(x) =; -1<x< 5. Show in a single space. 2x

A: Given

Q: The function g (x) is defined as follows: 2x - k 16x - 21 2x Xs 1 1 3 9(x) = a) Find the value of k…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: sin (5x) Evaluate the limit lim x→0 4х

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Q: A rectangle is to be inscribed inside the semi-circle with its base along the x-axis. The equation…

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Q: (11) Find the tangent line(s) to the parametric curve given by * = t5 - 4t3 y = t2 at (0, 4)

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Q: Hence, determine whether the function is continuous at x = 2x. ) Find the value of k such that the 5…

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Q: 3. Suppose f(x) dx = 8 , f (x) dx = -2, g(x) dx = 3 Evaluate the following integrals: a) 3f(x) dx =…

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