Use the power series E(-1yx", IxI < 1 to find a power series for the function, centered at 0. f(x) = In(x + 1) = x + 1 f(x) = E Determine the interval of convergence. (Enter your answer using interval notation.)

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A: We have to find the sum of series.

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A: According to our guidelines we can answer only one question or three subparts of a question. Other…

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A: Given problem:- Find the maximum value of ƒ (x) = ln(x−lnx) on the interval 1/e≤x≤e

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A: We can answer both the question as below

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A: The integration of the integral is csc52x.

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Q: TRUE OR FALSE 10. Addition and Simplification can be applied to part of lines of proof. 11. If p, q,…

A: Here is the solution

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A: Given :Principal = P2500Rate =535=285%Time : Nov 6, 1988 to April 11, 1989

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A: A detailed solution is given below

Q: 1 dx x² +1 e +

A: solution:-∫02ex+1x2+1dx=∫02exdx+∫021x2+1dx=ex02+tan-1x02=e2-e0+tan-12-tan-10=e2-1+tan-12     Ans

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A: Given the region is bounded by the f(x)=sinx2 and line x=π2 and x axis.

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A: As you have asked multiple questions so I have answered first question as per the guidelines

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A: We can find the partial derivative in the following steps.

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A: Given that we need to Sketch the grah of  y = 2x1/3 + x4/3  Now,  The graph is as follows

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A: Here, the given function is: g(y)=cos(y+1) To find the linear approximation of g(y) at y=y0=0 using…

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Q: •4 (ii) 2y dy dx.

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Q: find area between line y=-2+x and y=x^(1/2) and x-axis 26/4 O 23/6 O 36/2 O

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given…

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A: (3)f(x)=2x+3 if  x≠12     if  x=1limx→1-f(x)=limx→1-2x+3=5limx→1+f(x)=limx→1+2x+3=5f(1)=2it is…

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Q: 5 and 6

A: 5. ∫127*ln(3x)xdxSubstitute u=7ln(3x)→dudx=7x→dx=x7du=17∫12uduWe know that…