Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) = cos²(t)

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A: Given that   we have to evaluate ∫S∫ f(x,y)dS  and                                fx,y =xyS: ru,v =…

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: answer is in next step.

Q: 6.0 and a are each acute angles in standard 12 13 position. sin0 = and cosa = 3 5 a. Determine cos(a…

A: We need to determine given angles.

Q: 1. Using a compound angle formula, demonstrate that sin is equivalent to 2π 3 sin π 3

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Q: Evaluate ln(e2)   a. 2.712828   b. (2.71828)2   c. 2   d. 5.437

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Q: 68 3 (x + yz) dx + 2x dy + xyz dz, C consists of line segments (1, 0, 1) to (2, 3, 1) and from (2,…

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Q: 2. A ball travels in a circle at 3 radians/s and starts on the positive x-axis. How far away is the…

A: Let 'w' be the angular speed of the ball travels in a circle.  Thus, w= 3 radians/s.  Let 't' be the…

Q: 4. Determine whether each series is convergent or divergent. If it is convergent, find its sum. 2) Σ…

A: The given series, a) ∑n=1∞3n-12n+1b) ∑n=1∞sin1nc) ∑n=0∞2n+15n

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Q: Find all numbers c that satisfy the conclusion of the mean value theorem. f(x) = 2x2 - 5x + 1, [0,2

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Q: Which of the following series should be used to determine the divergence of the series Σ, V5n2+2n+4…

A: Given :- ∑n=1∞5n2+2n+4n

Q: Prob. 4 (a) (6 pciats) If h(x) = (1 + f(x))³, where f(1) = −2 and ƒ'(1) = 3, find h'(1).

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Q: find the limit if it exists at infinity lim=5x^2+7x-9/-6x^2+2

A: Given, limx→∞5x2+7x-9-6x2+2

Q: √9-x Consider the following double integral 1 = So So By reversing the order of integration of I, we…

A: Mark the limits on the graph and then reverse the order

Q: Find the radius and interval of convergence of the power series (−1)″ (x+2)" √n.3n n=1

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Q: 20. J 1 (x+25)√√x dx

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Q: Find the curl of the vector field F. F(x,y,z) = x sin(y) i - y cos(x)j + 5yz² k Part 1 of 3 It is…

A: The objective is to find curl F.

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

A: Given that a sequence which is defined recursively by the formula given below:-an=an-1+an-2-(i)…

Q: 3 A merry-go-round has a radius of 4 m and is spinning at a rate of 0.5π radians/s. Bill is standing…

A: Formula used: Circumference of circle = 2π×radius of circle  velocity =  angular velocity × radius

Q: 45. Which of the following is the Laplace transform of cos(2t)+2tsin(2t)? a. s^2/(s^2+4)^2 b.…

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Q: on (2.41. A(x) = Incorrect

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Q: Euler found the sum of the p-series with p = 4: 3(4) - Σ Σ n = 1 Use Euler's result to find the sum…

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Q: of sin (4) sin³2 x sin 2x dx

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Q: 3. Find the general solution of the differential equation y(4) — 4y" = t² +et.

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Q: Find the curl of the vector field F. F(x, y, z) = (2y - z)i + e²j + xyzk

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Q: LORAN (long distance radio navigation) for aircraft and ships uses synchronized pulses transmitted…

A: answer is in next step , i can only answer one question as per guidelines.

Q: 3x2+2 0 2x²+4x+3 So dx

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Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

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Q: (1) ਤ + x2 x2 + 3 dx (2) In 2 -e ex 1+e dx x +7 (3) --x-6 dx

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Q: Determine the total number of arrangements of the digits 173174561737 so that no 7s occur next to…

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Q: A goat that weighs 6 pounds at birth gains weight at the rate (a) Find the particular solution of…

A: Solution is given below:

Q: A breeding group of foxes is introduced into a protected area and exhibits logistic population…

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Q: 72. The volume of a sphere is increasing at a rate of 40 cm3 per minute. Find the rate at which its…

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Q: education. He has found a bank that will pay 9 percent interest compounded continuously. How much…

A: Topic:- algebra

Q: find the angle between the pair of vectors to the nearest tenth degree 7i-5j,2i-8j

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Q: 15. 1/√/2 X 1+ 4x4 dx

A: We need to evaluate :

Q: 2 i) [x² ( x + ²7 - 2²/1) dx x i) Ï 0 x³ - 8 x-2 dx ii) ii) f (x³ + 3x² + 1) e-2x dx xe xe1+x dx

A: Given:   i) ∫x3x+2x-1x2dx Expand   =∫x4+2x2-xdx Apply linearity     =∫x4dx+∫2x2dx-∫xdx

Q: (b)(is) Verify that the function satisfies the hypotheses of Rolle's Theorem on the given interval.…

A: Explanation of the answer is as follows

Q: Consider the following. u = (-2, -7, -5), V = = (-8, 3, -6) (a) Find the projection of u onto v. (b)…

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Q: e. Find the second derivaitve. f''(x) = f. Use parts b through e to identify maximums as points. g.…

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Q: Using De Moivre's formula demonstrate that sin(3x) = 3sinx − 4sin3x

A: Given that sin3x=3sinx-4sin^3x De moivres formula is (cos x+ i * sin x) ^ n = cos n*x+ i * sin n*x -…

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Q: Let R be the region in the plane bounded below by the parabola y = x² above by the line y = 2x. Then…

A: Use application of integral for finding the area of curve between two curves.

Q: In *In ecot³x dx feln sinx

A: We need to evaluate integral.