1 Evaluate. 5P3 • 6C4 900 300 150

Q: Given the series E n10 Which one of the following gives lim n=1(-10)+1 Select one: 3 10 1 None of…

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Q: Using decomposition into partial fractions, 3x2 + 2 dx J x(x2 + 2) is equal to

A: The objective of the question is evaluate the indefinite integral using decomposition of partial…

Q: |y = xx² – 4)

A: This is a problem of area calculation by region given. Based on the general formula and concepts we…

Q: Part 4: Solve the following problem. Show your complete solution. 1.) Find the equation of the…

A: A detailed solution is given below.

Q: sove the fowowing, using Lagrange Multipiiers: Maximize flR, Y. 2) solaject to x2 + Ax + a4 t 2 + 2…

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Q: Find the work done by the force field F(x, y, z) = xyi+ yzj+xzk or a particle that moves along the…

A: Given: Fx,y,z=xyi+yzj+xzkr(t)=ti+t2j+t3k

Q: For the following function f(x), find f(0) and f(2). if xs0 x2 f(x) = if 0 <x<2 x+3 if 2sxs4 4-x…

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Q: I. Find the equations of the horizontal and vertical Tangents. x3 + 3x? – y? = 0

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Q: x-1 y = log, x+1

A: We know, ddxlog(x)=1x ddxu(x)v(x)=v(x)u'(x)-u(x)v'(x)v(x)2 log(ab)=log(a)-log(b) log(a)n=n*log(a)

Q: For the differential equation (x -4)y" + (x- 2)y'+ 2y 0, the singular points are: O None of them x-3…

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Q: Determine whether the series is absolutely converger convergent or divergent. Please provide…

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Q: For some constant a, the following improper integral | (x2 – 1)e2xdx converges to converges to e2a…

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Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1) 2

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Q: a) Explain why the function f(x) = e#² is not injective (one-to-one) on its natural domain.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 3x+1 5) lim x+ 2x +5 2+Vx lim ²-3x 6) 7) lim 2-Vx

A: Limits

Q: test the convergence ad diivergene

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Q: -3 -8- -

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Q: Use the graph of y = fx) shown at right to determine whether fis continuous at 0. (-6,4) 41 94) Is f…

A: We can solve this as follows:

Q: 2x3 = (3xy + 1)2 Implicit Derivative with Solution (step by step using chain rule and product rule)…

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Q: In Exercises 5 through 18, sketch the given region R and then find its area. 5. R is the region…

A: The region bounded by the lines y=x, y=-x and x=1

Q: 1/5 2n'5 3) Use the Limit Comparison Test to determine whether the series V5n + 7n+7 n=1 is…

A: Given problem:-

Q: 1 Integrate

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Q: Express the limit as a definite integral on the given interval. -Дх, [1,4] (x;)2 + 9 lim i = 1 dx

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Q: The polar equation of the curve is expressed as r = 2sine + 2cose. area bounded by the curve.

A: To find the area.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Determine the values of a, b, and c for Ax) = ax + bx+c so that f") = 6x- 3 and A2) = -1.

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Q: 2. Find the average value of the function x2 In(x) for 1 5x<3 Show your work in evaluating any…

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Q: Using decomposition into partial fractions, 4x2 + 2 dx x(x² + 2) is equal to In|x (x² + 2)| + C…

A: Solution is given below:

Q: In(x®y®) = x² +y³

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Q: Using appropriate trigonometric substitution, dx xV4 – x² is transformed to S sin 0 d0 sec 0 d0 2 2…

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Q: provide a step by step solution to the following equation dy/dx + 2xy + xy⁴ = 0 answer: 1/y³ = -½…

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Q: Using Sandwich Theorem, the sequence 1 cos? n + 1 an = 4 - n converges to 4 converges to 2 diverges…

A: Given

Q: Ssec10dE

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Q: The position of a point at time t = 1 is (2, 4) and velocity of the point at time t is . Wha the…

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Q: Change from spherical coordinates to rectangular coordinates $ = 6. O z2= 3(x² + y²) O z2= 3(x²…

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Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: evail hupisuoɔ əui 8u the partial fraction decomposition for 5x² – 3 - f(x) (x³ – 4x²)(x² – 3x +…

A: We have to find out partial fraction

Q: nd the surface area of the plane ( 15x- 5z+20y=D35) if it is in the first octant

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Q: Given: R. 23 30° A R= 04 v3 02 v3 B.

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Q: Find the differential equation of a family of parabolas with an axis parallel to the x-axis. O y"y –…

A: Option A

Q: The integral dx – 4 3 1 Vx2

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Q: Let F(a) = f(x*) and G(x) = (f(x))". You also know that a = 2, f(a) = 3, f'(a) = 15, f'(a*) = 2 |3D…

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Q: 2) z= (1+t²)(3 - 2y); z' Ans: z' = -2(3t? + 3t + 1)

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Q: €) In VEx dx d) so sce x e Serx tumx dx

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

Q: 2x+5 Зх +1 5) lim 2х+5

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Q: Simplify the complex number. Express your answer in a+ bi form and include each step necessary in…

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Q: Using Sandwich Theorem, the sequence 2 cos? n + 1 an = 4 - diverges converges to 0 converges to 2…

A: Use range of cos x which lies in -1 and 1

Q: If 0 = Ø and R= 4/2, then F2 = %3D 4V2 F, F, V8 08 O 2 04

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Q: dy Suppose that x and y are related by the equation 2x - y = 1 and use implicit differentiation to…

A: The given equation 2x2-y2=1

Q: Eliminate the arbitrary constants on the given equation: y= Ae" + Bre 2y +y=0 O y =-y" + 2g

A: To eliminate the arbitrary constant.