Evaluate the following integrals: 1. S (cos x – sin x) dx 2. ſ cot²x dx 3. S (sin x + x) dx

Q: 1- x dx 3.

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

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

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A: Find f'(1)

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: Obtain the differential equations satisfied by the given puiiicular 3. y = e5x - 3x - x2 4. y = e3x…

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Q: Q.1) The general solution of the equation y e' cosA a) y(t) =c, +c; x +c,¢ ' de' cosa Re' sinx b) y…

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Q: xチ+1=4 DIDX= 2-2y (ost) X= 3サ-3 *キーに h で3,0) サ=2メー オー×ポーカ toノー4) メッとナ+ム メーリー3

A: Explanation of the answer is as follows

Q: Find and classify all critical points of the function defined by h(x,y)=x^3−3x+3xy^2.

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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…

Q: Find the first three nonzero terms of the Maclaurin expansion of the function. f(x) = 8 cos TX ...…

A: The Maclaurin series is given by  f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: 4. The derivative of a constant is 5. The derivative of a of two functions is the denominator times…

A: This question is based on Basics of differentiation.

Q: Evaluate the following integrals using Trigonometric Substitution: x-1- 16x dx x 2. dx 9 dx 25t2 - 1…

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Q: dx 4xvx²-16

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Q: -Sune +1

A: This question is based on solution of Trigonometric equation.

Q: Зx+1 5. f(x) %3D 3x2+2

A: f(x)=3x+13x2+2Differentiate…

Q: y =, x = 1, x = 4, and y = 0 is revolved about the y – axis.

A: Let's find.

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Q: mine the value(s) of x where the slope of the tangent line is horizontal. Use exact valı…

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Q: Question 1 Determine the inverse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9) (b) 352+5s+1 (d)…

A: Let's find.

Q: Find the inverse transform, indicating the method used and showing the details: 2s - 10 -5s 1. s3 3s…

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Q: -dx x2 +9 I x3 +ar-23 ton- (특) +C a. 3 b. 1 x³ t qx + 27 tam " ) + C b*3-9*+27€an )+c C. d.늘-9x- 2구…

A: Using substitution method, integration is done.

Q: I. Evaluate the following integrals. 3.x5 dx V2 – x3 1. - 2* + e2" sin(2") dx sin(2") 2. 2x + 3 dx…

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Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

A: Given problem:- Use differentials to estimate the amount of paint needed to apply a coat of paint…

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Q: Suppose z is a function of x and y, and z^xe^6y=y2+x2. Solve for ∂z/∂x and ∂z/∂y. [b]

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Q: S 23x26 ++16 dx

A: Here we have to integrate the given Integral.

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider A = (0, 4, 2), B = (6,0, 0) and C = (3,0, –1). (a) Find the unit vector in the same…

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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

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A: We need to choose correct option.

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Q: 1. In the chart below, you are given a formula. Name the formula. Formula Name of the formula/what…

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Q: sove the focowing using Lagrange Multiptiers: Maximi ze flx, Y, 2) solaject to x2 + y + 22 =1 Ax +…

A: Method of Lagrange Multipliers : 1.) Solve the system of equations .…

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Q: S In(5 + Vr)dr

A: This question can be solved using the concept of integration by substitution and integration by…

Q: Sunecose - Sune=0

A: The objective of the question is solve the given equation.

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A: Given that the series the  To find the Power series

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A: Given:∫02(x-3)ex2dx

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Q: 3s 14 82-4s +8 - 3e cos 2t + 4e2" sin2t 3et cos 2t –4e2" sin2t - Option 1 O Option 2 4e2t cos 2t +…

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A: Given

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Q: dx 5x2 + 16

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Q: a²z B. For each of the following functions z, find a² z and ду? a² z дх? дудх" дхду" 1. z = 2x2 –…

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