Consider the polar curves Cı : r = 1+ cos 0 and C2 : r = 2 cos 0, and let R be the shaded region as shown below. 2 C1 C2

Q: Find the derivative of y with respect to t. y = In (t) dy %3D dt

A: Given function y=lnt9 we have to find derivative of y with respect to t. ln is natural logarithm…

Q: 4 x² +4x-5 dx= find the new limits of integration. Using Trigonometric Substitution f(e) de x+2 TT O…

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Q: 15х2 — х3— 43х - 19 The integral | can be rewritten as (x + 1)²(x² – 6x + 13) Ах + B C D lax² + bx +…

A: Follow the procedure given below.

Q: Which of the following is Inx – 6x + 18| + arctan(- (x – 3)) +C equal to? 2 – 6x + 18 x - 3 V 2 In…

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Q: Given the function f(x) =2+3x - x³. Determine the intervals where f is increasing or decreasing,…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 11 cos(t)i + 10 sin(t)j +…

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Q: Find the length of the spiral r = 80 for 0 < 0 < 3. (Use symbolic notation and fractions where…

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Q: 5. Use differentials to approximate the value of V(3.01)² + 2(0.99) – 3 in four decimal places.

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Q: |(x² + a) 5 5x The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers.…

A: Given:        ∫5xx3+x2+4x+4dx Apply linearity:     =5∫xx3+x2+4x+4dx Factor the denominator:…

Q: If R is the region enclosed by x-axis, y = -3x and x = -2, then evaluate the following double…

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Q: dh _10. A cylindrical piston with fixed radius r = 3 cm is being compressed so that How h =- dt fast…

A: Given

Q: 2) Given: f(x) = x+sin(2x) over the interval (0,7) a) Use a sign analysis to find the relative…

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Q: Find the general solution of ydy/dx =2/(3x2). O a. y?/2 =-2x/3+ C O b. y/2=-2/3x + C O c. y?/2 =…

A: 1. ydydx=23x22. The slope of the curve is 2x+1, passes through the point -3,0

Q: Question * Given csc(0) = -2 and 0 E Quadrant III. Then the values of cot(0) and cos(0) are: cot (8)…

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Q: 5. Suppose that f(n) satisfies the equation 5. f(m + n) = f(m) + f(n) – 2f(mn) for all integer m,n…

A: The objective of the question is computing the value of f(n).

Q: Find exactly T(t) and N(t) for x = e*cost, y = e'sint, z = e' for t = 0. [Choose the correct…

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Q: Find the area in the first quandrant bound by the parabola y

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Q: 3 3 What is the value of the integral 2x ydydx ? Select one: O 4/83 O None of these O 83/4 O 4/81 O…

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Q: ナ+sy'+by =4et も

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Q: 3 2 3. Vxydydx = Vxdx Vydy Select one: O True O False

A: This question is related to double integral , we will solve it using given information.

Q: dx 1- cos 2x

A: The given integral is ∫dx1-cos2x Now,        cos2x =1-2sin2x       ⇒  1-cos2x=  2sin2x…

Q: 7. S 8x³ e** dx il ww be 7dx 8. J sec x esinx bne

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

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Use the algebraic substitution and solve the integration.

Q: Find the derivative of the function y=(4x+1)^5(3x+1)^-4

A: We can find the derivative as below.

Q: 5. Let f be a function satisfying the following properties: continuous on R \ {0} • f(-1) = -3 •…

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Q: 10) For y=v+8, use the differential dy to approximate Ay when x changes from r=1 to x=0,97

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Q: What will you factor out from the integrand of ] csc°(3x)dx so that you can transform it to its…

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Q: 2х — 5 lim 4x

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Q: %3D Determine the speed along a parameterized path c(t) = (6 sin¬'(t), 3 tan¬(1)) at time t = 0…

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Q: (7) If 4.5* = 97, an approximate value of x is (A)x = log(97) × 1.987 (C) x = In(97) z 4.575 (B)x =…

A: 7.    4.5x=97 Note:      Multiple questions are given, we are answer with only one question. if you…

Q: 5. Use differentials to app. .. the value of V(3.01)² + 2(0.99) – 3 in four decimal places. o 5.…

A: I am attaching image so that you understand each and every step. Let x= length of box y=width of box…

Q: (1 – x²)dx eTextbook and Media 2) V You answered correctly! Move on to the next part to add to…

A: According to guidelines we solve only first question.

Q: 1. Find the area of region bounded by the curves y = x² and line y=x. %3D

A: We have to determine area of region

Q: Using integration by parts, which of the following options is true x arcsec x dx ? xdx A. * Arcsec x…

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Q: 2 Evaluate V4-x² dy dx using polar 2x-x2 Coordinates.

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Q: give the equivalent cartesian coordinates of ρ = π

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the area enclosed by the lemniscate with equation r = 289 cos(20). Choose your limits of…

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Q: Find the total area enclosed between y = x and y = x over th- %3D interval [-1,6]. NOTE: Enter the…

A: Here, to find the area enclosed by y=x3 and y=x over the interval [-1,6].

Q: 2. A solid right cylindrical cement block of volume 97 ft³ is to be made, and then painted except…

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Q: To evaluate x² /1-x² dx using trigonometric substitution, what is the new integral in terms of 0 ? A…

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Q: 43x2-2x dx . | Evaluate x + 2

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Q: 2.S Ver eax dx Sve

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Q: 3x² +7x+28 f(x) x2 + x+7 A Using partial fraction, evaluate x3 + x2 +7x aX the decomposed fraction…

A: The objective of the question is evaluate the indefinite integral in partial fraction.

Q: +00 dx II. Evaluate the improper integral x(In x)²

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Q: 4. Suppose U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {3, 4, 5, 6, 7}, B = {all multiples of 3} and C =…

A: U=1,2,3,4,5,6,7,8,9A=3,4,5,6,7B=all multiples of 3C=all multiples of 2

Q: If f(x) = (4x – 2)² - (3x² + 6)", find f'(4).

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Q: Let C be a curve that is defined by x = 4 sin t and y = cos t, t E 0, 27]. Determine (a) the time…

A: Let C be a curve that is defined by x=4sint and y=cost, t∈0,2π. x=4sint⇒dxdt=ddt4sint=4cost…

Q: 7.) Find the area inside the graph of r-7 + 3cos(e) and to the left of the y-axis

A: As per bartleby guidelines we only give first  questions answers.

Q: Find the length of the arc of the parabola  x^2 = 4y from x = -2  to x = 2.

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

Q: 7 -4 Consider the surface x'z* + sin(y zª) + 9 = 0. Use implicit differentiation to find the…

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