Find the derivative of the function. f(x) = In(sinh(x)) f '(x) =

Q: Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

A: Given problem:- Use Green's theorem to evaluate ∫c (xy + y2 )dx + x²dy  by the curve y = x and y =…

Q: cos (x) tan (x) dæ

A: I have stated the used formulas in the solution

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

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Q: Using trigonometric substitution, what is dx ? A sec + C 2x2 Vx² – 9 +C sec-1 6x2 none of the…

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Q: 100e0.05z thousands of Over the next 5 years, a company projects its continuous flow of revenue to…

A: profit = revenue - cost here  revenue for next 5 year R(x) = 100e0.05x R(5) = 100e0.05(5) R(5) =…

Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.

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Q: The angle below measures 5.4 radians, and a circle is centered at the angle's vertex. 5.4 rad,…

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

A: We will evaluate the Integral of left hand side and right hand side then we will compare them .

Q: Find the average value of the function on the interval. Give an exact answer. f(x) =  1/(x-7)^2…

A: For average value of f, we need to integrate in the given interval.

Q: Evaluate the integral 3. 2х cos(xy)dydx 2

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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: 2) Find the cartesian eauation for the olar curve r=tan e sece ×ニy )yニxと 2.

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Q: Put 3s+4 (s-2)(s²+7) in partial fractions.

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Q: Is this statement true or false?

A: Given a continuous function f on a closed interval [a, b] and f(a) &gt; 0 and f(b) &lt; 0 or f(a)…

Q: Find the polar equation of a line parallel to the line r cos (0 = 1 and lying at a distance d = 5…

A: The given line is: rcosθ-π5=1. A line parallel to it, will be of the form: rcosθ-π5=k

Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x,y, z) = 2x²…

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Q: Use polar coordinates to evaluate the integral where R is the region that lies in the second…

A: follow the procedure given below.

Q: What is the volume of the region R = ((x. y, z) e R'1 sxs 3:2 sy S 4:3 sz5 5)? %3D Select one: O…

A: Volume of the region R is given by volume=∫13∫24∫35dzdydx

Q: 4-x III. Evaluate dx. V16-x2

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Q: Continuity of a function on an interval: Show your solution, graph (use GeoGebra) and identify if it…

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Q: Decide which of the following regions has n () in area = lim tan 2n 2n i=1 without evaluating the…

A: To decide which of the regions has the given area.

Q: B/Using the following table, find f(x) as polynomial in x: -1 0. 3 6. F(x) -6 39 822 Good Lup

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Q: lim - Va +1

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Q: Please use definite integral in solving for the area. a. y = Vĩ and y = x3

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Q: Whale and Kanmuro are two islands located in the Chimera archipelago. These two are separated by a…

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Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Find the area A of the part of the circle r = 13 sin(0) + 13 cos(0) in the fourth quadrant. (Use…

A: Here we have to find the area A of the part of the circle r in the fourth quadrant.

Q: d²y and dx2 Find dy then simplify whenever possible. dx 1) y = 3t5 – 2t x = 4t3

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Sketch the region whose area is represented by the integral Só Suz dxdy.

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Q: JV-x² + 4x+5 Consider dx. Using trigonometric substitution, what is the integral form in terms of 0?

A: We have to determine  integral form of given question

Q: x + 20 g(x) = { 3Cx + K if – 2 < x За — 2K if x < -2 | if 1 < x -

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: What is the slope of the line 0 = (Use decimal notation. Give your answer to three decimal places.)…

A: Slope of a line θ=a is given by m= tan(θ)=tan(a)

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: EXERCISES answer page 338, letter B. (COPY & ANSWER) В. In exercises 1 to 8, refer to the triangles…

A: To answer the given questions using the given triangles. where hyp=hypotenus

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: 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: 'he graph of a periodic function f is shown below. f(4) 4 \1.57 3.14 4.71 6.28 a. What is the period…

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Q: an onine SOcial group nad 3o0 miion Tme uently, new me m(t) = -3.3t2 + 14t + 230 million members per…

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Q: 7) A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A: Given: A spherical balloon is to deflated so that its radius decreases at a constant rate of 15…

Q: sin x dx 1- sin2 x 4. cos x dx 2+3 sin x 5.

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Q: Put 3s+4 (s-2)(s²+7) in partial fractions.

A: Inverse laplace transform of 3s+4s-2s2+7

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

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Q: 27. 12f(r) – g(x)] dx = 28. Ư(x) – g(3)]dx =, 29. (4g(x) – 3f(x)] dx = 30. f) + 39(x)] dx =

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Q: A flu epidemic hits a college community, beginning with five cases on day t = 0. The rate of growth…

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Q: 4. If f(t) = 3 sin(4t + 0.12) – 2 cos(3t – 0.72) determine f'(t) when t 1 5. Evaluate when x 1,…

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Q: Given x sin (yz) + y³ cos (xz) + z sin (xy) = v3. Find əx (a) implicit differentiation, (b) by…

A: a) Implicit differentiation: We will treat y as constant.…

Q: Evaluate the integral 3 2x cos(xy)dydx 2

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Q: 1 -x dx = u v- Sx sec xtan Svau Using Integration By Parts, Find UV- X sec ec- x dx 1 1. x sec 1.…

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Q: 14. (x + 3x – 1) dx 15. dx tU +1) -G² – 1)]dy 16.

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Q: to the South Coast Air Quality Management District, the level of nitrogen dioxide, a brown gas that…

A: Here,  A(t)=0.03t3(t-7)4+60.2, 0≤t≤7