Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. S² (t = 12²) at g(s) =

Q: Sketch the region of integration and evaluate the following integral. SS= 4+ R -dA, R= {(r,0):…

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

Q: Evaluate the limits. Enter DNE if the limit does not exist. a) lim g(x) = x-9 b) lim g(x) = X-9+ c)…

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Q: = Find the angle between A (3,-2, 3) and B = (1, -3, -3).

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Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

A: To find the antiderivative F of f that satisfies the given condition. To check the answer by…

Q: Find the equation of the tangent line to the curve y = 4 sin z at the point (7,2). The equation of…

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Q: Where does f(x)=- have a critical point, which is not an extremum? O O O x = -1 x=0 x = √√3 x = 1 x³…

A: From the above function , we get 3 critical points at X=0, -√3 and √3 and two point where function…

Q: 38. 32 (-1)k k=0 (2k + 1)³

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Q: Sarah is asked to find the maximum value of a function. Not having a complete understanding of the…

A: If we want to find the maximum or minimum values of a function then follows the steps mentioned…

Q: A region bounded by f(x) = -x + 4, y = 0, and x = 0 is shown below. Find the volume of the solid…

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Q: dy 8. = dx 1 x+y+1

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Q: is there no numerical answer to this question?

A: Let's evaluate given integral.

Q: If sin a = 0.806 and cos ß = 0.718 with both angles' terminal rays in Quadrant-I, find the…

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Q: Find the integral. √(x + 1)e 6x² + 12 е 12x dx √(x + 1)e 6x² + 12x dx = [

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Q: A hemispherical tank, placed so that the top is a circular region of radius 6 ft, is filled with…

A: answer is in next step.

Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: 5. The general solution of (D² A. y = (C₁+C₂x)e+C3 C. y = (C₁+C₂x)ex+C3e-2x +2D+1)(D²+4)y=0 A) A cos…

A: To find out the general solution of the differential equation.

Q: The figure shows the velocity function for motion along a line. Assume the motion begins with an…

A: Answer: As per guidelines we can do only first 3 subparts of question and solution is given below:

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

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Q: Let f be the function defined by f(x) = sin 2x + cos 7x and let g be the function defined by g(u) =…

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Q: 5. Evaluate each of the following inte x² (53+1)3 (5 (a) da

A: We have to find the solution As per guidelines we have to solve one question Please repost other…

Q: 18 0-17 ¹8 cos(x¹8+18) Question 6 Find the total differential for the function w = Odw - 262³ y sin…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

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Q: Use the Comparison Test to determine whether the series converges. Σ k = 1 1 5k5 +6

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Q: Question 3 Given the following, complete the questions below: A= B= 2 a. Perform the transposition…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: ) .  Consider a minimal threshold value for a species to survive, T. One way to add in this factor…

A: answer is in next step.

Q: question 8 please

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Q: Draw the directional field for the differential equation. y' = y2 − 1   What can you say about the…

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Q: Find the area of the region bounded to the right by x = 4 - y and to the left by x = y. +57 +5 543-2…

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Q: Suppose that the position of a particle is given by s(t) = 2t³ + 6t + 9. (a) Find the velocity at…

A: Topic = Derivative

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Q: Determine the y-coordinate of the centroid of the shaded area shown. 15" Parabolic. 4" Answer: y = i…

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Q: Use properties of logarithms to condense the logarithmic expression below. Write the expression as a…

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Q: Q5. (a) (i) (b) (c) (ii) Express sin 2x Express cos 2x Show that in terms of in terms of sin x Solve…

A: Given problem:- (a) (i) Express  sin 2x in terms of sin x and cos X.(ii)  Express cos 2x in terms of…

Q: Consider the basis S = {V₁, V₂} for R2, where v₁ = (1, 1) and v₂ = (1, 0), and let T:R2 R2 be the…

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Q: A region bounded by f(x) = x, y = 1, and x = 4 is shown below. Find the volume of the solid formed…

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Q: Use the Integral Test to determine the convergence or divergence of the following series, or state…

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Q: Find the solution to y' =    2y satisfying y(0) = 15.

A: Solve the following

Q: ).  Use separation of variables to solve the differential equation explicitly for u. du dt = 9 + 9u…

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Q: Given the vector field F(x,y) = [x/((x^+y^2)^(3/2)), y/((x^+y^2)^(3/2))], Find a fucntion f(x,y)…

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Q: here are two regions bounded by the line y=x and the curve y=x^3, one in the first quadrant and…

A: Given problem:- There are two regions bounded by the line y=x and the curve y=x^3, one in the first…

Q: If the number of fruit flies F increases at a rate that is proportional to the number of flies…

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Q: Find the area of the region bounded to the right by x = y + 2 and to the left by x = y². 543-2 1…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: cit ++ -3 it -15- -30 -45 -60 -75- -90 -105 -120- -135- <x< N ton For the above quartic polynomial…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: 3) .  A population of deer inside a park has a carrying capacity of 200 and a growth rate of 4%. If…

A: To find the population of deer at any given time, P(t).

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Q: A cylindrical can is being filled at the rate of dh = 3t², h(t) describes the height of the…

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