Math 106 A and B ←− circle your section Quiz 05 page 1 02/17/12 Name
1a. The following table has several (zero-th, first, second, third, etc.) derivatives for the function f(x) = (x+ 5)3/2.
Fill out just as much of the last two columns of this table as required to find find the third degree Taylor polynomial
approximation P3(x) of f(x), in powers of x+ 4, that is, with “base point” a=−4. NOTE: Keep all the ck’s as fractions
(that is, in the form p/q) in reduced form (Don’t convert them to decimals)
Write your “assembled” polynomial in the blank space to the right of the table.
k f(k)(x)f(k)(a)ck
0 (x+ 5)3/2
13
2√x+ 5
23
4
1
√x+ 5
3−3
8(x+ 5)−3/2
49
16 (x+ 5)−5/2
2. For each of the following integrals, choose the best way to “do” the integral from the list below. Write the letter of
that choice in the box next to the integral. The first one is done as an example. If two choices are equally valid, write them
BOTH in the box!
Zx+ 2
x2+ 2x+ 1 dx Z Z(sin3x)(cos4x)dx Z(tan4x)(sec4x)dx
Z(sin4x)(cos4x)dx Zdx
x2√x2+ 4
Choices:
Z) Let u=x2+ 2x+ 1 A) Let u= sin xB) Let u= cos xC) Let u= tan xD) Let u= sec x
E) Use “half angle” formulas F) Let x= 2 sin tG) Let x= 2 cos tH) Let x= 2 tan tI) Let x= 2 sec t
3. Suppose in some trig substitution problem, the substitution used was x= 4 sin tand the antiderivative in terms of tis
t/8 + cot t+C. What is the answer in terms of x?
