4. S ( 12 x³ + 15 x - 20 ) dx

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A: As per the guidelines I am supposed to the first question among multiple questions. So I am solving…

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

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Q: 5) Sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If…

A: Note: Rate of change of volume of conical pile is equal to rate of change of sand pouring from the…

Q: Use Green's theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

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Q: Using Integration By Parts, x sec - x tan x dx = %3D

A: Use integration by parts.

Q: x +5 Given the function g (x) find g' (x) x² +6x O 8' (x) = x* +6x³ +5x² +30x x² (x+6)? O 8' (x) 2x3…

A: Given, gx=x2+5x2+6xDifferentiate…

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: xy + y² dx dy Find the general solution of

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: + Inx y(In2x – Iny)

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Q: Question 1 π 2x Evaluate the integral cos(xy)dydx 4

A: ∫45∫0π2xcosxydydx

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Q: What will you factor out from the integrand of tanx sec'x dx so that you can transform it to its…

A: To factor out a term such that the given integrand becomes integrable.

Q: Sally is standing on a wharf that is 5m above the surface of the water. She is pulling on a rope…

A: Use the trigonometric ratios and application of derivative.

Q: Q5/Find the Laplace Transform 3-f(t) = sint cos t

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Q: ] Let D be the region bounded between x + y = 4 and x + y = 9 that lies within the second and the…

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Q: The integral 15x* - x* - 43x – 19 (x + 1)2(x2 – 6x + 13) can be rewritten as

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Q: Sketch and use a double integral to find the area of the region R bounded by the lines: y = 0, y = x…

A: Graph of the given fucntions

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

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Q: Find the approximate change in volume of a cube of side 'x' inches caused by increasing its sides by…

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

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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: (x Using a suitable trigonometric substitution, the resulting integral in terms of V9x²+4 Consider e…

A: Given problem:-

Q: d d Calculate ri(t) · r2(t)] and rı(t) × r2(t)] first by differentiating dt dt the product directly…

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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: The area bound by the curve y^2 = 12x and the line x = 3 is revolved about the line x = 3. What is…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given,   r(t)=cos(πt)i-ln(t)j+t-16k

Q: 2.) Find the area between the curves y? = 2x and y 6-x

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Q: b) Evaluate the following integral by using the polar coordinates R where Ris the enclosed region by…

A: solve the double integration

Q: A clothing manufacturer has the marginal profit function MP(x) = 40 - 0.02x, Os xs 100 (in dollars…

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Q: dx Vx²+2x+5

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Q: x +6 (a) Find dx. (1– 2x)(x² +3)

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

A: We can find the derivative as below.

Q: Let R = {(x, y) ER214 < x? + y < 9}. By inverting to polar coordinates: %3D y? %3D Vx? - + y2 Select…

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Q: S, f(2)dx+ f(x)dx = 21. 23. S f(G)dr + J, f(x)dx =, = <p(x)f f – xP(1)f !!

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Q: If you are going to evaluate the integral f cos x v9 + 25sin-x dx using trigonometric substitution,…

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Q: To evaluate dx using trigonometric substitution, which of the following is the new integral form in…

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Q: Find the centroid of the region R bounded by the graphs of y x and y 1. 1) Which of the following…

A: To find the area of the region R.

Q: For what values of a and b is the following function continuous at every x? - 10 XS-3 f(x) = < ax-b…

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Q: Sketch the curve y = x4 - 6x2 and show intercepts, maxima and minima and points of inflection

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Q: _12. What is the maximum directional derivative Daf of the function f(x,y,z) = x – y² + z² at the…

A: Let's find.

Q: Evaluate the definite integral 3e-0.05r dr by the following steps: (a) Determine the indefinite…

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Q: discuss and sketch the graph of the given function f (x) = e" + x %3D

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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: Does this mean the sequence is always convergent?

A: We can take limit of the sequence.  limn→∞an=limn→∞-1n-1nn+n

Q: Consider the following piecewise function: 3x + 6A ЗАх — 7В if — 3 < x < 3 х — 12B if x < -3 9(x):…

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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: (x – y)dx + xdy = 0.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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: 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: Please use definite integral in solving for the area. y = |x| – 2 and the x axis

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