Math help
DA.777
1217_e3_spr16.pdf
Math 1217 Ex III SPR16 Due 5/6/16
Name_______________________________________________
SHOW ALL WORK FOR CREDIT!!!! If you use L’Hopital’s rule, make sure to specify
the corresponding indeterminate form. Each problem is worth 15 pts.
THIS IS A TAKE HOME EXAM. PLEASE MAKE SURE TO WORK ALONE.
1) Evaluate the following limit using L’Hopital’s rule, if necessary.
(a) lim x
ln
ln
x x
x x
(b) 2
0
4 2 lim x x
x
Math 1217 Ex III SPR16 Due 5/6/16
Name_______________________________________________
SHOW ALL WORK FOR CREDIT!!!! If you use L’Hopital’s rule, make sure to specify
the corresponding indeterminate form. Each problem is worth 15 pts.
THIS IS A TAKE HOME EXAM. PLEASE MAKE SURE TO WORK ALONE.
(2) 1
8
8 ( 8)lim x
x x
= ?
Math 1217 Ex III SPR16 Due 5/6/16
Name_______________________________________________
SHOW ALL WORK FOR CREDIT!!!! If you use L’Hopital’s rule, make sure to specify
the corresponding indeterminate form. Each problem is worth 15 pts.
THIS IS A TAKE HOME EXAM. PLEASE MAKE SURE TO WORK ALONE.
3) The combined perimeter of a circle and a square is 16. Find the dimensions of the
circle and square that produce a minimum total area.
Math 1217 Ex III SPR16 Due 5/6/16
Name_______________________________________________
SHOW ALL WORK FOR CREDIT!!!! If you use L’Hopital’s rule, make sure to specify
the corresponding indeterminate form. Each problem is worth 15 pts.
THIS IS A TAKE HOME EXAM. PLEASE MAKE SURE TO WORK ALONE.
4) Find the point on the graph of the function f(x) = 4 5x closest to the point (9,0).
Math 1217 Ex III SPR16 Due 5/6/16
Name_______________________________________________
SHOW ALL WORK FOR CREDIT!!!! If you use L’Hopital’s rule, make sure to specify
the corresponding indeterminate form. Each problem is worth 15 pts.
THIS IS A TAKE HOME EXAM. PLEASE MAKE SURE TO WORK ALONE.
5) A rectangle is bounded by the x- axis and the semi-circle y = 2
25 x . What length
and width should the rectangle have so that its area is a maximum?
Math 1217 Ex III SPR16 Due 5/6/16
Name_______________________________________________
SHOW ALL WORK FOR CREDIT!!!! If you use L’Hopital’s rule, make sure to specify
the corresponding indeterminate form. Each problem is worth 15 pts.
THIS IS A TAKE HOME EXAM. PLEASE MAKE SURE TO WORK ALONE.
(6) Find the volume of the largest right circular cone that can be inscribed in a sphere of
radius r.
Math 1217 Ex III SPR16 Due 5/6/16
Name_______________________________________________
SHOW ALL WORK FOR CREDIT!!!! If you use L’Hopital’s rule, make sure to specify
the corresponding indeterminate form. Each problem is worth 15 pts.
THIS IS A TAKE HOME EXAM. PLEASE MAKE SURE TO WORK ALONE.
(7) A rectangle is bounded by the x and y axes, along with the graph of the function
y = (6‒x)/2. What should the dimensions of the rectangle be so that its area is
maximum?
