iven g(x) X 1 = 5₁° dt. Determine g'(0). t² + 1

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A: We have to convert rectangular coordinates and polar coordinates according to the given information

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

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A: Given that sin θ < 0 and tan θ > 0

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Q: Problem 2: exactness of the DE 3x(xy-2)dx + (x³ + 2y)dy = 0

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Q: C. Evaluate the following inverse Laplace transforms. 2. C-1 ((s+3)4 2S-1 s²-2s)

A: To evaluate the following inverse Laplace transforms.L-16s+34-2s-1s2-2s

Q: - Given two Complex numbers 2 = 1 + j₁ and w = 2-4 j, which of the following. Options equals 13/0…

A: Given: z=1+j,w=2-4j To find : zw

Q: V. Find the third derivative: 1) y = 10 tan(x) - 2 cot(x) 2) y = x³ - x² sin (x) 1 3) y = 2 sin(x)-4…

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

Q: A ski run on Giant Steps Mountain in Utah is 1475 m long. The difference in altitude from the…

A: GivenA ski run is 1475m long and the difference in altitude from the beginning to the end is 350m.…

Q: Find the limit algebraically. lim h→0 (f(-2+h)-f(-2)) h where f(x) = -4x²-x+1

A: Given function:- fx=-4x2-x+1

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 6 - Lºcos…

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Q: We can use L'Hopital's Rule to calculate " O True lim x18 O False x 2 (x - 2) (x + 2) although it is…

A: Given query is to find the limit.

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Q: Determine whether the integral is convergent or divergent. 3 30 [³ convergent 3-x O divergent Submit…

A: Given query is to find integral converging or diverging.

Q: (1 point) If f(x) = 3x² + 4x + 2, find f'(5), using the definition of derivative. f' (5) is the…

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Q: 2. Given x³ + y³ = 3xy, find the equation of the tangent line at (2/3,4/3). I'm looking for your…

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Q: bacteria culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria…

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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: Evaluate (6x +4√/y) ds where C is given in the accompanying figure. ...) 1- (0,0) y=x (1,1) y=x² X Q…

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Q: You invest $49,010 in an account earning 5.26% APR, compounded daily. How much total interest is…

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Q: (a) (b) y 10 X-C 8 6 4 2 lim f(x) = x+c+ lim f(x) = (c) lim f(x) = X-C 2 4 Is the function…

A: We have to determine the limit  using the given graph and c=9

Q: Find the gradient of the function g(x,y) = xy² at the point (2, -4). Then sketch the gradient…

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Q: 15.4, 4

A: We will find the required area of one leaf.

Q: Find the profit function if cost and revenue are given by C(x) = 192 +1.7x and R(x)=6x-0.05x2². The…

A: Step 2 complete solution

Q: Find the future value for the ordinary annuity with the given payment and interest rate. PMT=…

A: Given query is to find the future value.

Q: Calculate for w = xyz. By

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: C. Evaluate the following inverse Laplace transforms. 3 1. C-1 (125 + -1 (125 + (+52) (s+5)²)

A: L-1{ 125s6 + 3( s + 5 )2 } Formula used L-1{ 1sn } = tn-1( n - 1 )!L{ e-atf( t ) } = F( s + a )L-1{…

Q: Determine the indefinite integral = 1 - 3 sin² r cos³ r dr. I =

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Q: VERFADER Find the direction angles of the vector. (Round your answers to three decimal places.) U =…

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Q: Find the divergence of the following vector field. F = (5x²yz, - 4xy²z, -5xyz²) The divergence of F…

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Q: Part II. 1) y = cos(2x) sin(x) 2) y sin²(x) cot²(x) 3) y = 2 cos(x) − 6 sec(x) +3

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Q: Find the solution of the following differential equations. Show your soluti 5. (4D³-4D2+ D-1)y=0

A: The given differential equation is: 4D3-4D2+D-1y=0   So, the auxiliary equation is: 4m3-4m2+m-1=0

Q: Do not use a calculator for this problem. Find the x-value where the maximum value of y = sin x 3x²…

A: We have to find the x-value where the maximum value of y = sin x- 3x2 occurs.

Q: 1. of fl) = 4x + 4/₁ find f (2), using the definition of derivative. f (2) is the limit as x-…

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Q: How do you find the radius of convergence of a power series cn (x − a)"? n=0

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Q: A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.…

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Q: In Flatland there are four cities, Abbott, Banchoff, Charlie and Dimension. The distance from The…

A: We can solve it by Dynamic programming algorithm.

Q: If yo is the particular solution of dy 8x³y, y(0) = 4, da find the value of yo(2). 1. yo(2) 2. yo…

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Q: The sets F and E are given below. F = {a, f, g} E = {e, g, j}

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Q: Solve the initial value problem given below. In your solving process, make sure to (1) write the…

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Q: An arithmetic sequence has a15 = 86 and a34 = 200. Find a150. an = a₁ + (n − 1)d -

A: NOTE: Refresh your page if you can't see any equations. . it is given that