MAT251 - Final Exam - Questions

7/27/2019 MAT251 - Final Exam - Questions

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Submission: Final Exa.rn

Decide whether each of he following areproperties of integrals.j [f(x)- g(x)]dx=j f(x)dx- Jg(x)dxSelected Answe r:

Question 6Decide whether each of he following are properties of ntegrals .j [f(x) g(.r)}.tx = j f(x)dx Jg(x)dxSelected Answer. -

Question 7Acylindrical tank ofheight 8 mand radius 3m is filled hall-waywith water.Approximately howmuch worit is needed to fXJ'TlP the wa.er to the rin of he tank?Selected Answer:

Question 8Find the general sntiderlvative of f(x) = cos 22:c .Selected Answer:

Question 9"Given a.= (n), we can usethe Integral Test to determ ine whetherLOn is convergent W

Selec ted Answer:

Question 10Given that a.> 0 and bn> Oforall n, and that l., where L'#'Oand L'#'


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f dx I -(xl - I )2, ~ -

Question 12 7.5 out of 7.5Whichof he following Is a sokJ1ion d thedilfenlntial equation ~ = 6% ?Selected Answe r.

Question 13f 3 dr -4x2- 9 -Selected An swe r:

Question 14Whichof the following represents the area between the curves f(x) =-x2+ 2x + 3andg(x)=.r + I on the Interval [-I , 2)?Se lec ted Answer:

Question 15Suppose- have a rod that Is 6meters long, with density function p(x)= 2x+ 3.What Is thecenterof maaa of tha rod?Selected An swer:

Question 16Partldes A and Bare located on lhax..,.;s . The masses and positions dlhe pa!1idesare gillen by:

ms= Sgrams xa=10What is the centerof mass of this two partlcfesys18m?Selected Answe r:

Question 17

points

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!Find the arc leng1h of the curvey = x2 tromx= tox= 4.Round your answer to three decimal places.Selected Answer: -

Question 18 7.5ou t of 7.5If Cx) Is an even function ,decidewhether eachof the following are true or false.Jj (x)dx= .J(x)dxSelected Answer:

Question 19

I.;sint ,If g(.r) = I 7 ' han g (.r) =Selected Answer:

Question 20f.J< sintIfg(x)= 1 ~ / , t h a n g'(x)

Se lected Answer:

Question 21If (x) Is an even function, decide whethereach of he following are trueor false.JJ


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Selected An swe r:

Question 25 7.5 ou t of 7.5For what values ofx does (x+2)' converge?

-1n3" .JnSelected Answer. -

points

Question 26 7.5 out of 7.5points ( ~ ) =-1 3Se lec ted Answer: I

Question 27 7.5 out or 7.5The Maclaurln sarles tor a function f(x) IsSe lected Answe r:

Question 28The net change ln y =f (x), as x changes from a to b, is given by:Se lected Answe r:

Question 29Whi


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est Submission: Final Exa.rn

Question 32Match eaeh of tho lntograls on tho loftwith the corresponding solution on the rightQueslion Se lec ted MatchJ ecxdx IJ scxdx I --Jco


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TestSubmission: Final Exam- - - - - -

Question 39Jxe2xdx=Selecled Answer.

Question 40Forwhldl of he folowing sertes Is the Ratio Test InconclUsive (that is, it ails to give adeftnhe answer)?

~ ( - 1Y'.Jn+lI. .t..= l + n3

~ -2)"+ IIll. .t.. ,--=1 "n

Se lec ted Answer:

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0 out of 7.5 points

MAT251 - Final Exam - Questions

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