1. f(t) = 4 2. f(t) = e³t

Q: Use Green's Theorem to evaluate the following line integral. ffdy-go y-g dx, where (f.g) = (6x²,3y²)…

A: Let's solve given integration.

Q: Which of the following expressions does sin(x - y) - sin(x + y) simplify to? O-2(cos x)(cos y)…

A: The answer is given in step 2

Q: Differential Calculus Direction: Differentiate the following trigonometric functions: Part I. 1) y =…

A: As per Bartleby guidelines we only give first three question answers. Please repost for other parts.…

Q: A circle has a radius that is decreasing at a rate of 12 mm per minute. What is the rate of change…

A: Let Radius = r Area = A As we know that A = π( r )2 drdt = -12π

Q: What is the area of the region bounded by the curve y = sin x and the x-axis on the interval x = π/2…

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Q: The function h is defined piecewise as follows. (x+2)²+2 if x -3 x+2 h(x): Find the following…

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Q: Use the Divergence Theorem to evaluate (5x + 11y + z²) ds JJS where S is the sphere x2 + y2 + z2 =…

A: We have to use the divergence theorem to evaluate the integral.

Q: Compute the percent relative error in computing the area of a square whose side is measured with an…

A: We need to find error in area.

Q: C. 1. Determine the area of the given region. XX y sin 2x-1 -2 y = sin x y=sin 2x 2x

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Q: centered at x = 0 for f when 1 (4x + 1)¹/2 * f(x) = 2. T3(x) = 1 + 2x - 6x² + 20x³ 3. T3(x) = 1-2x +…

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Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth. r(t) =…

A: Given vector function:- rt=t2i+t3j

Q: Which Vector Integration technique/theorem should you use for the problem below? Please use complete…

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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: Find the value(s) of ß for which y (t) = cos(ßt) satisfies y” + 100y = 0

A: Given that yt=cosβt satisfies the equation y''+100y=0. We have to find the values of β.

Q: Two particles travel along the space curves r(t)and u(t). A collision will occur at the point of…

A: Two particles travel along the space curves rt and ut. A collision will occur at the point of…

Q: x² dx + y(x - 1)dy = 0

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Q: Find the values of c such that the area of the region bounded by the parabolas y = 25x² - c² and y =…

A: Given y = 25x2 - c2y = c2 - 25x2First find intersection points  25x2 - c2 =  c2 - 25x250x2 = 2c2x =…

Q: Consider the given vector field. F(x, y, z) = 8xyezi + yze k (a) Find the curl of the vector field.…

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Q: a. Determine whether (F(x,y)) is a conservative vector field? b. If the vector field is not…

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Q: z Find the Taylor polynomial på for f(x) = xe at z = 2.

A: we have to find the taylor polynomial P3   for function f(x)=xe-x  at  x =2   f(x) = xe-x   ⇒f(2)=…

Q: x+3 20 Find the linearization of f(x)=1-S 2² x+3 The linearization of f(x) = 1 - S 8 8 20 2+t dt at…

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Q: How long will it take $3,000 to grow to $25,000 if it is invested at 7% compounded monthly? years…

A: Given: Initial amount, P=$3000 Final amount, A=$25000 Rate of interest, r=7%=0.07

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

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Q: ·S√2t³t² dt = dr 8 √2x³ - x²

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Q: Evaluate the integral. 12 tan ³x dx 12 tan ³x dx=

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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: 2x -5 dx x²-2x-8

A: I=∫2x-5x2-2x-8dx

Q: 2² Calculate Rn for f(x) = - R + 6 on the interval [0, 4] and write your answer as a function of n…

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Q: Find the gradient of the function f(x,y)=6y-5x at the point (8,2). that passes through that point.…

A: Please see the below picture for detailed solution.

Q: Solve the system by elimination: 4x - 3y-6z = 1 x-y-6z=5 6x - y = -11 Express your answer as an…

A: Given system of equations 4x - 3y -6z = 1 x - y - 6z = 5 6x - y = -11

Q: da xy² = x

A:

Q: OA. The resulting matrix is (Simplify your answer.)

A:

Q: Find the interval of convergence of the se- ries Σ n=1 an Vn+3

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Q: B. Evaluate the following Laplace transforms by using the formulas listed in the table of Laplace…

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Q: Find the interval of convergence of the series. (x − 7)″ 2+8n Σ n=0 OA. 2<x< 12 OB. -1≤x≤15 O C.…

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Q: Use 1 + tan² x = sec² x to evaluate tan xsec4 xdx

A: To evaluate the given integral

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: Assume the nominal interest rate for an account is 6% per year. Find the effective annual interest…

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Q: Define R as the region bounded by the graphs of f(x) = 3x² − 3x + 3, x = 0, x = 1, and the x-axis.…

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Q: MY NOTES The guy wire supporting a 100-foot tower has a tension of 530 pounds. Using the distances…

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Q: 2. When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01…

A: Given: Rate of increase of radius = 0.01 cm/min Radius = 50 cm

Q: 4. L{cosh √at}

A: Given expression L{ coshat }

Q: C. Evaluate the following inverse Laplace transforms. 2-1 (1-25 +(353) 1.

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Q: Mary Branson invested her summer earnings of $5000 in a savings account for college. The account…

A: Given Principal amount ( P ) = 5000Rate ( R ) = 6.5 % Time ( t ) = 6 months =0.5 years

Q: Olve 2 cos² (x) + cos(x) - 1 = 0 for all solutions 0 < x < 2. List solutions in exact form, and…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the following for the given equation. r(t) = (t² + 3t)i + (t²- 3t)j (a) r(t) = (b) r"(t) = (c)…

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Q: Let f (x)=5. Which of the following statements is true about the graph of f?

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Q: 01 3 2 16-s² ds= (Type an exact answer.)

A: We are required to evaluate∫04316-s2ds

Q: Evaluate the integral. (Use C for the constant of integration.) √x² - 81 2 X |v +8 dx

A: Given,           ∫x2-81x4dx

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