My final answers for HW 5 which was handed in today, and comments about what I am looking for:

Final answers:

#1.  e

(They should take logs and then use L'Hopital's rule)


#2.  2*pi2

(They should integrate 2*pi*x*sin(x) from x=0 to x=pi)


#3.  NOTE that there are several possible correct answers that may look different.

-ln( csc(x) + cot(x) )

ln( csc(x) - cot(x) )

ln( cot(x) - csc(x) )

I don't care whether they write ln| | or ln( ).  In Math 242 we are sometimes sloppy about that detail.


#4.  Most students will probably have

ln(x-1) - ln(x+1)  or  ln( (x-1)/(x+1) )


#5.  Most students will probably have

-2*ln( (x+1) / sqrt(x^2-1) )

or 2*ln( (x-1) / sqrt(x^2-1) )

or 2*ln( (1-x) / sqrt(x^2-1) )

They will probably use their answer for #3 in #5.


#6.  Some students will have already answered #6 in #4 or #5.
Basically, using algebra and rules of logarithms, the answers for #5 can be rearranged to look like the answers for #4.


#7.  Final answer is 40/3.  Note that they don't have to do trig substitution. Many students will, but they can also use the substitution u = 16-x^2.


#8.  Final answer is (1/2)ln(3/2) (which can of course be written different ways). Numerical answer is around 0.2027.

In #8, they can just use their answer for #4 or #5.