In Exercises 39-42, find dy/dx. - Sv V2+cos³ t dt 39. y = 40. y = -7x² [T²³v 2 V2+cos³ t dt

Q: 6. Consider the following graph of the function f(x) = cos(x). Draw on top of the graph to indicate…

A: Here we have given a function: f(x)=cosx. a) The limit that will compute the exact area represented…

Q: Determine of the following series { (-1)" n=1 the convergance и 2n+1 or divergence of each

A: We need to determine whether series converges or diverges.

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1200 feet apart. As the…

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Q: Example 1: Consider the graphs of the functions f(x) and g(x) given below. Find each of the…

A: "Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Determine whether the given point (x,y) is on the unit circle. Nin Ο No OYes QUESTION 20 Use the…

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Q: Find the centroid of the region bounded by the graphs of the functions y = 2x² x² +1 Y = The…

A: y=2x2, y=x2+1

Q: The series Σ n=1 convergent. (-1) " n 0.9 Select one: O True O False Give your reasons is absolutely

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Q: 43. an = 2¹/n

A: By using the appropriate limit laws and theorems to determine the limit of the sequence or to show…

Q: 2 X 2 [√³² L √ ² - ²³ √ x² + ²³² dy da dx 0 X

A: ∫0√2∫x4-x2x2+y2dydx

Q: and a tangent vector at point P. 2 166. (x² + y²)² = 9 (x² - y²), P(√2, 1)

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Q: 10. Find the linear approximation of the function g(x) = √√/1 + x at a = 0 and use it to approximate…

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Q: Suppose [*, f(x)dx = 2, ſª f(x)dx = 7, [*f(a)da = 9. [²² [² (2ƒ(x) — 7)dx= f(x) dx

A: ∫-18fxdx=2 , ∫-12fxdx=7,∫58fxdx=9

Q: Find the centroid of the region bounded by the graphs of the ㅠ - 18 || functions y the origin. The…

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Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 5,…

A: a(t)=2t+5, s(0)=4, v(0)=-5 Find s(t).

Q: Marginal Cost A division of Ditton Industries manufactures a deluxe toaster oven. Management has…

A: we have given the marginal cost function C'x=0.0006x2-0.14x+25 Daily fixed cost is = $900

Q: Find the anti-derivative of the func f(x) = = sin (₁+x) - Solve initial Value Problem f(x) = *+^, Y…

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Q: Solve the differential equation. 5√xy dx = dy dx = 2, x, y>0

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Q: Determine whether the given point (x,y) is on the unit circle. Nin 21 No OYes

A: This is question of calculus  here one point is given  we have to verify that this point is on unit…

Q: 12. Practice similar Help me with this Use the Integral Test to determine whether the infinite…

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Q: 7. Let F = x² + ²² − x² + y² j Find the line integral of the tangential component of F, from (-1,0)…

A: We have to evaluate the line integral. According to our guidelines we can solve only one question…

Q: 1. The electrical power p(t), in kilowatts, being used by a household as a function of time t, in…

A: p(t) = power in kilo watt t = time

Q: equation, in slope-intercept form, of the line tangent to the curve with param + 4t and y = Int at…

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Q: 1. Find the general anti-derivative of each of the following functions. (a) f(x) = 3x² - 4x + π (b)…

A: General antiderivative of f(x) is given by F(x)+c , where c is constant and F'(x)= f(x) Simply we…

Q: 1 (a - b) In (a − x) (b - x) X *)] = [K₂ t]

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Q: Given u = 5i + 4j and v=4i - 3j, determine -9u — v.

A: Same cofficient addition and subtraction of two vector

Q: Find the total mass of a 1 meter rod whose linear density 39 kg/m for 0 ≤ x ≤ 1 (x + 1)² function is…

A: The linear density function of a 1 meter rod is:ρ(x)=39(x+1)2  kg/m     for  0≤x≤1

Q: 25. an = ln 12n+2 −9+4n

A: Given :an=ln12n+2-9+4n

Q: 1. 2. Find f'(x) and f"(x). Determine the following Domain a. b. x and y intercepts t. The critical…

A: derivative calculated by differentiation with respect to x

Q: 4) IF F(2) = 20 and F'(x) 24 for all valves OF X, how small can F(5) Possibly be? Use mean value…

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Q: Find the differential of the function. = x ln(y² + 6) dz= Z = ]dx + ( [ Jdy

A: Given: z=xln(y4+6) We are required to find: The differential of the given function.

Q: Recall the Chain Rule and how it can be applied to find the derivative of a composite function. In…

A: As per our guild line we are supposed to answer only 3 subparts of a question.

Q: The initial and terminal points of AB are given below. Write the vector in component form. A (-5, 2)…

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Q: Find the trigonometric form of the complex number shown below. √3+ i O 2√3 (cos+ i sin ) O √2 (cos+…

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Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the…

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Q: Newton's Law of Cooling says that the rate at which a body cools is proportional to the difference…

A: The temperature Ft of the body at time t after being introduced into an environment having a…

Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 7,…

A: We have acceleration function, need to find position function using integration.

Q: 61. an = nsin RIS n

A: We find the limit of given sequence.

Q: Evaluate the following indefinite integral. de = +0 ds +C

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Q: L (4 + √36-x²) dx

A: Evaluate the definite integral  We know that the formula int_a^b f(x) dx=int_b^a f(x) dx

Q: (b) 2 1 √2 t√²-1 dt (c)

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Q: 4 -2 -2 -4 h(x). 10 X

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Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Remember the…

A: we have integration =∫5x2+20.5x3+0.6xdx

Q: Find the dot product of the vector pair. u = and v =

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Q: Given u = 5i + 4j and v=4i - 3j, determine -9u - v.

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Q: 5) The function g(x) is always negative and has an average value of -12 over the interval 0 ≤ x ≤ 5.…

A: To find the area between the curve y = g(x) and the x-axis over the interval [0, 5], we need to…

Q: Given: (x is number of items) Demand function: d(x) 5120 √x Supply function: s(x) = 5√√x Find the…

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Q: Find the most general antiderivative of the function. antiderivative.) F(x) = f(x): = 2x4 + 6x³ +³ -…

A: To find the most general anti-derivative of the following function. fx=2x4+6x3-xx3, x>0

Q: Consider the series Answer: L = n=1 5" (n+1)4²n+1* Evaluate the the following limit. If it is…

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Q: Where is the function continuous? Differentiable? Use the given graph of g to answer the questions m…

A: From the graph y=g(x)=3-(x-1)20≤x≤23-(x-3)22≤x≤4

Q: 1 1 9. C₁=1+₂+3 ²+ Cn + + 1 n

A: