Please see the attached file for the fully formatted problems.© BrainMass Inc. brainmass.com September 19, 2018, 10:53 pm ad1c9bdddf - https://brainmass.com/math/calculus-and-analysis/taylor-expansion-remainder-157111
Please see the attached file. Note: I think the formula of h(x) is wrong, so I corrected it and proved by using the new formula.
a) Show that =0 for any
NOTE: I think the formula for h(x) should be
Otherwise, the following statements are FALSE.
We consider three cases.
Case 1: k=0
Case 2: k>0
Let y=1/x. Then when x tends to 0, y goes to infinity. Hence,
This is the type of . By the L'Hospital rule, we have
Taylor Expansion and Remainder are investigated.