| cos ?x sin'x dx can be evaluated by factoring sin'x as (sin²x) ²sinx and transf sin²x into 1- cos?x

Q: 2-y QI) Evaluate the integral f dx dy using polar coordinate

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Q: Which of the following is the Taylor series expansion of the function -x2 with center at 0. f (x)=e…

A: Given problem:-

Q: 4. Find the Laurent series of the following function : f (z) = (z + 1)(z + 3) 1 region 2 < |z – 1| <…

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Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at æ = for f(x) = cos(x). %3D T2(x) must…

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Q: PART II. Find the derivatives of the following expression, solution must be presented. (3 marks…

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Q: Evaluate the following integral using Partial Fractions Method: x³ + x? y = dx х2 + х — 2 -

A: Follow the procedure given below.

Q: (e) Suppose that the functionf is represented by the power series f (x) =1- +(-1)*. - -- +... 2 4 8.…

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Q: Consider the integral 5 x (z° +1) dx. In the following, we will evaluate the integral using two…

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Q: Water is pouring into a swimming pool. After t hours, there are t + sqrt(t) gallons in the pool. At…

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Q: Solve the particular solution of the equation dy/dx = 3x² - 2x, when y=2 and x=-1.

A: We can solve the given problem as follows:

Q: Which of the following yields the value 318? 3 (8х + 7у) dxdy 0 °0 (8x + 7y) dydx 0 °0 none of the…

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Q: Find h'(x) if h(x) = x³e*sin x. O a. h'(x) = 3xe*sin x + x'e*sin x + x'e*cos x 3X, O b.h'(x) =…

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Q: DO NOT include spaces in between characters. And, DO NOT include dy/dx in your answer. dy Determine…

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Q: Which of the following yields the value 3187 (8r+7y)dudy (8r+7y)dydx (8r+7)dudy O none of the oices

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Q: 3rd derivative of y sin 3x

A: Here we have to find the 3rd derivative of           y = -1/sin(3x)

Q: Step 1 In pert (a), it was found that the two planes were 200 miles apart and getting closer at the…

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Q: Q4/ solve the equation by Newton -Raphson Method: F(x) = x* - 5x + 65 , start at x =2, accuracy…

A: Let's find.

Q: Find the value of e which is defined as the angle between j+k and i+j_ None of the choices 4 프2 프3

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Q: 1. S(5x4 + 2x – 1)dx

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Q: Question 5. Find the Laplace transform of the following function by using the integral definition of…

A: Given problem:-

Q: Consider z=e (*3+y2) Evaluate dx2 O (6r2+ 3x)e (*3+y2) (9x4+6x)e (x³+y²) (6x4+ 9x) e (x³+y²)

A: Topic = Derivative

Q: dy Find the general solution of 2x² = a? + y? dx %3D

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Q: For what values of x do the tangents to the curves y = (1 +x')² and y = 2r6 have the same slope? X =…

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Q: Use the Midpoint Rule for the triple integral to estimate the value of the intergral. Divide B into…

A: Note that, 0≤x≤4, 0≤y≤8 &amp; 0≤z≤4 generate the cube. And, the mid-points of the cube are:…

Q: 4 4-y Q3) Evaluate triple integral , S S dz dy dx

A: I have stated the used formulas in the solution

Q: Find the saddle point/s of the function f(x, y) = x² + y° + x®y+ 4 O a (4,0) & (-4,0) O b.(E -1) &…

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Q: For item # 6, use the product rule. 6.) f (x) = (x³ – 1)(4x + 5) %3D | x+3 7.) f (x) = 5х-2

A: Here we have to differentiate the given functions.

Q: Q5) Find volume of body bounded by z² + y² + x² = 9.

A: Explanation of the answer is as follows

Q: Give the VALUE only. No need to include the unit. * Let s, =15r +10r +20 and s3 = 5t + 40f , t 2 0,…

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Q: Evaluate the following integral using Partial Fractions Method: x3 + x? y = dx %3D x2 + x – 2

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Q: |x= 8| f (x) = Evaluate the left-hand limit of as X8. 16- 2x O 1/2

A: Given,            fx=x-816-2x as x→8To find : Evaluate the left-hand limit of the given function.

Q: Evaluate the integral: (3si + 9s²j + 4k) ds

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Q3) Evaluate triple integral (x - y²)dz dy dx.

A: tripple integral  First we will integrate w.r.t z and then w.r.t. y and then w.r.t. x.

Q: 4. S cot?x dx

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

A: Let's find.

Q: Use the difference table to predict the next term in the sequence. Show your complete formula.  1.)…

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Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: Question For the function given below, which statements concerning Rolle's theorem are true? —3х - 1…

A: This question is related to Rolle's theorem, we will solve it using given information.

Q: a. Neither I nor II

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Q: Find each of the following indefinite integrals.  c. Z (r+2)^2/r^3 dr

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Q: Consider the series 0 n=1 2+n3 For what values of p does it converge? I. p> 1/2 II. p< 2 O l only O…

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Q: J1 (3x -1)3 * tvt2 +1 dt

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y = 4.

A: Set up the triple integral and solve to get the desired volume.

Q: Q3) Evaluate triple integral f , (x2 -y²)dz dx dy.

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Q: "u,V.w are three vectors such that each is incined at an angle of 4 with the other two, and that lul…

A: To find the scalar product of two vectors with the given conditions.

Q: Je* cos (7e*) cos (4e*)dx Evaluate: @ --co (3e*) -cos (11e') + C (3e*) – -cos (11e*) +c A 6. 22 ®…

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Q: Q5) Find volume of body bounded by z? + y2 + x2 9.

A: Given that - x²+y²+z²=9 =&gt; (x-0)²+(y-0)²+(z-0)²=3² Clearly which is a sphere with radius,r= 3…

Q: hich of the following choices do the alternative ways for writing an iterated triple integral match?…

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