Use the series representation for cos x, cos x = 1 – + to find the following three items: 6! 1- A power series representation for x cos (교2): 2- A power series representation for fa cos (x2) dax; 3- An approximation using four terms of a series for the number o x³ cos (x2) dx.

Q: What is the approximate value of x in the figure below?* 723 58 427 3244 ft. 3169 ft. 820 ft. O 3322…

A: Find your answer below

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Q: Hwe Find dw and dw for the following functions

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Q: statements is NOT true?" a = 230, b = 150, C = 95° The length of the third side is 25.13 unite The…

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Q: What is the maximum value of f(x)= 2x4+16x3+40x2+64x+7 on [-8,-2]? a. -57 b. 4 096 c. -121 d. 2…

A: Given: fx=2x4+16x3+40x2+64x+7 ; x∈-8, -2   As we know that; The Power law; ddxxn=nxn-1

Q: he vectoi the given maghitude and the same direction as u. Magnitude Direction ||v|| = 19 u = (0, 2,…

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Q: 4. Solve the second order differential equation given by 2 dt2 3z = 4c", z(0) = 0, dt dr(0) 0. dt

A: We will solve the second order differential equation.

Q: ocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial…

A: We are asked to find the height of the Rocket

Q: For the function glven below, use algebra to evaluate the limits lim f( メー→+ lim f(x), and limf(x)…

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Q: Which of the following is equivalent to cos (60° + 0) + sin(30° + 0)? cos 0 + v3 stn e cos e O…

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Q: S e2x sin 2xdx

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Q: Ina swimming pool measuring 90 m by 40 m, 150 men take a dip. If the average displacement of water…

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Q: Consider the following. u = -9i – 2j - 4k, v = 4j + 4k (a) Find the projection of u onto v. (b) Find…

A: Explanation of the answer is as follows

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A: Given: Here, M=2x-2y2, N=12y2-4xy. Notice that ∂N∂x=-4y=∂M∂y. So, the function is exact.

Q: Solve bernoulli equation (dy)/(dx) - y = x * y ^ 2

A: Given problem:- Solve bernoulli equation (dy)/(dx) - y = xy2

Q: Solve the given initial-value problems. te dx +(y-1)dy=0; y(0) 0 4.43.

A: identify the differential equation and solve it.

Q: Evaluate by separation of variables. dß %3D и(1 — и?) sec? р du 2 tan B+ sin 2ß = C – (1 – u?)? 2u?…

A: To solve the given differential equation.

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: Which of the following is equivalent to cos 0-2 cos 0 sine 1-sin 0+sin²0-cos²0° tan 0 cot 0 O Option…

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Q: | cos 3y dy 4.

A: I=∫ cos6(3y) dy3y=tdy=t3Integration by parts;∫uv dx=u∫v dx -∫ dudx ∫vdx dxI=13 ∫ cos6t…

Q: 4. Find the equation of the tangent to h(x) = x´sin(2x) at x = 1 [no unit circle needed]

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Q: ind the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: Given: u=3  θu=8v=1 θv=3

Q: If f(x) = e*sinh x, what is f'(x)? e*(cosh x- sinh x) O Option 1 Option 2 e*(sinh x - cosh x) 2e2x…

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Q: Which of the following is not equivalent to sin 0?

A: We are asked to find which is not equivalent to sinθ

Q: A solid spherical steel ball, 20 cm in diameter, is placed into a tall vertical cylinder containing…

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Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

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Q: what is the minimum value of f(x)=3x2-18x+25 a. -2 b. 3 c. 6 d. -18

A: Given  f(x)=3x2-18x+25

Q: In trigonometric substitution where the integral involves va? + u², what must be the value of the…

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Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: the length of a child's square-based jewellery box is 5 cm more than its height. the box has the…

A: Topic  = Algebra

Q: Solve for the following application of first order differential equations. Show your solutions. 5. A…

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Q: This subject is DIFFERENTIAL EQUATION. SOLVE THE FOLLOWING APPLICATION PROBLEMS 2. The population of…

A: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

Q: Which of the following is equivalent to cos 0? cos 0(1+ tan? 0) sin 0 + tan 0 1+ sec 0 O Option 1 O…

A: Checking all options by simplifying.

Q: 4. The graph below depicts a function g(r). Its one asymptote is indicated in red: 4 -5 -4 -3 -2 -1…

A: Find your answer below

Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

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Q: 1. 9. 2

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Q: =D1 || |

A: I am attaching image so that you understand each and every step.

Q: ind cylindrical coordinates of the point with rectangular coordinates (3, –3, –7).

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Q: y^2= (x^2 + 2x)/ x-1 find the x and y intercept, symmetry, region/scope, asymptotes, critical…

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Q: Find dy for the following expressions: dx а) y = x5 In(3x) b) у %3D 2 cos + 2x3 3x2 + 7x + cos (x) y…

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Q: 3. Scse*x dx

A: The objective of the question is evaluate the indefinite integral.

Q: y = |x|, y = x² – 1, x = -1, x = 1 - г2 — 1,

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Q: (b) If a > b and c > 0, then ac > bc.

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Q: Funetion Values. Find Re f. and Im fand their values at the given point z. f) = 1/1-2) at 1- i 2) at…

A: Since we have the function                                             fz=11-z then we have to find…

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

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Q: Question Select your answer. Find the value(s) of the constant k so that f(æ) = kx² – 5x + 1 and…

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Q: Find the gradient of the function at the given point. f(r, y) = 3x+52 +1, (2, 1) %3D O 3i+10 O 3i+5j…

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Q: Which of the following is not equivalent to cos(0 + 0)? cos 8 cos 0- sin 60 sin 0 1- 2 sin? 0 O…

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