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Math 106 A and B — circle your section Quiz 05 page 1 02/17/12 Name_S Usgertel soln la. The following table has several (zero-th, first, second, third, etc.) derivatives for the function f(x) = (a +5)°/?. 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(zx) of f(x), in powers of x + 4, that is, with “base point” a = —4. NOTE: Keep all the cx’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. yey zh 2 (xs) + ve ¢%)23!= = 7% a)eteden Nore fhe Une L Kh, peed nt Jo) > © “34° e J b Ma ok bl were tly the (int ate 1p” Ze “ 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! Plx)=-2 5(x¥)* > z+2 in? 4 4 4 / aed / (sin? 2)(cos* 2) dx [B (tant 2)(sect2) de [C / (sin‘ 2)(cos* 2) de [E i zr H Choices: Z) Let u=a? +20+1 A) Let u=sing B) Let u=cosr C) Let u = tane D) Let u = secx E) Use “half angle” formulas F) Let « = 2sint G) Let « = 2cost H) Let x = 2tant I) Let a = 2sect 3. Suppose in some trig substitution problem, the substitution used was z = 4sint and the antiderivative in terms of t is t/8 + cot t+ C. What is the answer in terms of 2? h yes hare snt 28 =F xX 6 m& hap wp vith x= Isnt , ue fae Ss 4” hup hha? the thang, 4 now (a4 x => ade = ([/6 - x* L next , ct t = SE loo, Sint =e t= aesil%l) so FINALL: et lot t +C become. etal) rn: 
