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[answered] 1) 2) 3) 4) 5) 6) 7) Find the area of the closed region bou


Hi ,Please could you help me with some of this pratice problem.


1) 2) 3) 4) 5) 6) 7) Find the area of the closed region bounded by y = x2 and y = 2x ? x2.

 

8) The area enclosed between y = 1, y = 2?x, x = ?, and x = 1 is revolved around the x-axis.

 

Set up, but do not evaluate, an integral to find the volume.

 

9) Set up, but do not evaluate, an integral for the length of the curve y = x sin(x) from x = -? to

 

x = ?. 10) The curve y = x4, from x = 0 to x = 5, is rotated about the x-axis. Set up, but do not evaluate,

 

an integral to find the area of the resulting surface.

 

11) Find a formula for the inverse function f -1(x). 12) Find f ?(0), the derivative evaluated at x = 0. 13) State whether the sequence converges or diverges. If the sequence converges, find its limit. 14) Determine whether the series converges or diverges. If it converges, find its sum. For problems 15-18, determine whether each series converges or diverges. Write down which

 

test you are using.

 

15) 16) 17) 18) Determine whether the series is absolutely convergent, conditionally convergent, or

 

divergent. Write down which test you are using. 19) Calculate the Maclauren series for f (x) to the x2 term, using the definition of a Maclauren

 

series. 20) Integrate a known power series to find a power series representation for ln(5-x) and its

 

interval of convergence. Express your answer using sigma notation.

 

Hint: 5 - x = 5(1 - x/5)

 


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