What is the first term of the Maclaurin expansion of y = 8 e -0.5t cos t?

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Q: 1. The figure shows the graph of a function f (x) with domain 0 < x < 3. Which of the following…

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Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

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Q: 3s – 14 - s2 – 4s + 8 - 3e2t cos 2t + 4e" sin2t 3et cos 2t – 4eª sin2t Option 1 Option 2 4e" cos 2t…

A: Given: Fs=3s-14s2-4s+8   As we know that; The inverse Laplace transform identity. 1).…

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Q: vertical asymptote z=0 S'(z) > 0 for z -3, (z # 0) f"(z) 0 for z > 0

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Q: 3s + 2 4s2 + 12s + 9 3 5 4 + Stezt 2 5 4 3 Option 1 Option 2 3 2 4 +te -tet 4 5 3 e O Option 3 O…

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Q: Exercise 4 * Suppose the following data points are generated by a smooth function f(x): 1/6 1/3 1/2…

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Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

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Q: 2x determine the derivative of f(x) = 3 X

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Q: .4 dx 2 Vx2-2

A: Given:        ∫24dxx2-2 Apply trigonometric substitution:    substitute x=2sec u and dx=2 sec u tan…

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Q: Use Method of Variation of Parameters: [D² - 8D + 16]y = e4Xsec2x

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Q: 1. Evaluate the given line integral, (-y,x – y) · dR, where C is the upper part of x² + y? = 4 from…

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Q: Find the Inverse Laplace of the following 6s – 4 s2 – 4s + 20 2e-24 cos 4t + 8e " sin4t Option 3…

A: Explanation of the answer is as follows

Q: 2. Suppose z is a function of a and y and tan(V+ y) = e*. Determine dz dz and 2

A: Suppose z is a function of x and y  tan (√(x + y)) = ez^2  We have determine ∂z/∂x and ∂z/∂y

Q: VII. Use Lagrange Multipliers to solve the following: Maximize f(x, Y, z) = 4x + 2y + z %3D subject…

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Q: Write the expression into single interval L, f(x)dx + L° f(x)dx = 5. f(x)dx – S° f(x)dx =. 4.

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Q: For the function f (x) = x4 - 4x3 + 5, find the local and absolute extrema and any points of…

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Q: 6s-4 82-4s+20 2et cos 4t + 8et sin4t None of the Choices Option 2 2e 2t cos 4t + 8e-24 sin4t 6e 24…

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Q: 2. For the parametric equation shown below, determine the value of (dyldx) and (d²y/dx?). x = 3t? –…

A: To find dydx&amp; d2ydx2 using the given parametric equations.

Q: 2sec? (w) – 8 csc(w) cot(w)

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Q: dx Vx-4x-7 S- -dy y2-8y+5

A: The given integrals are' 1)1/sqrt(x2-4x-7)  2)7/(y2-8y+5).

Q: 1 (s+1)(s2 +1) + cos t - sin t) + cos t – sin t) O Option 4 O Option 2 5(e-cost + sin t) 5(-e+cos t…

A: L-1{ 1/(s2 +1)(s+1)} expand it  L-1 {-s/2(s2+1) + 1/2(s2 +1) + 1/2(s+1)} L-1 s/(s2+1) = cos(t) L-1…

Q: 7 In the interval T, 27|the equation sin x = 8 (a) has no solutions (b) has one (and only one)…

A: Solution of (sinx)^2 = 7/8.

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Q: ²+² +1) d + a (a – 2y) dy = 0 %3D

A: Given problem:- Find the solution of the given differential equation:  (x² + y² + 1) dx + x (x - 2y)…

Q: a?z B. For each of the following functions z, find a2z and ду? a²z дх? дудх' дхду" 1. z = 2x2 – 5xy…

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Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: 2) w = 2yTan(2x + y) – 3xSec(x²y³) %3D

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Q: 6. Evaluate the integral /: a sec (x²) tan(x²)d.x. sec*(x²) tan(x²)d.x. sec (x²) tan(x²) (a) + C 6.…

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Q: az and ду az A. For each of the following functions z, find ax 1. z= sin3x cos4y 2. z = tan- (2) 3.…

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Q: ) Eliminate the arbitrary umstants of y= C, + C2 e ** + C3 e 3x

A: The given equation is y=c1+c2e2x+c3e-3x. We have to eliminate arbitrary constants c1, c2, c3. Since…

Q: The average value of f(x, y) over the rectangle R = {(x,y)| a<x< b, c <y <d} is 1 fave (b – a)(d –…

A: The given expression is: fave=1b-ad-c∫∫Rfx,ydA And fx,y=xy2x2+1 and R=x,y|0≤x≤1, -3≤y≤3 So, a=0,b=1…

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Q: Find the Laplace Transform of the functions 1. e-2t (cos t + 3 sin t)

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Q: 2. y=x² - 4x and y=-x² +2x. y² = x and x² –2x+3y= 2. 3.

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Q: Evaluate each limit: x +x-30 a) lim x-3 x-6x+5 3-1-4x b) lim X-2 x+2 x+3 c) lim x→-3 Vx-5+2

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Q: oint) Use the graph of f(x) shown below to find the following integrals.

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