Barrons AP Calculus

(B)

(C)

(D)

(E)

36.(A)

(B)

(C)

(D)

(E)

37.(A)

(B)

(C)

(D)

(E)

(A)

(B)

(C)

(D)

(E)

2 x −   2x^2    +   8x^3    −   16x^4   +   ·   ·   ·

2 x −   4x^2    +   16x^3   +   ·   ·   ·

    ·   ·   ·

    ·   ·   ·

The set of  all values  of  x   for which       converges   is  only    x   =   0

|x| =   2

−2  <   x   <   2

|x| >   2

|x| ≥   2

The  third-order     Taylor  polynomial  P 3 (x)     for     sin     x   about   is

Let h   be  a   function    for which   all derivatives exist   at  x   =   1.  If  h(1)    =   h′(1)

=   h′′(1)  =   h′′′(1) =   6   ,   which   third-degree    polynomial  best    approximates    h

there?

6   +   6x  +   6x^2    +   6x^3

6   +   6(x −   1)  +   6(x −   1)^2    +   6(x −   1)^3

6   +   6x  +   3x^2    +   x^3

6   +   6(x −   1)  +   3(x −   1)^2    +   (x  −   1)^3

Part    B.  Directions: Some    of  the following   questions   require the use of  a   graphing    calculator.

NOTE:    Because     of  the     abilities   of  graphing    calculators,    Taylor  Series  and     convergence     are

largely  tested  in  a   No  Calculator  environment;    as  such    we  offer   only    a   few     calculator-active

multiple-choice questions   here.

Which   of  the following   statements  about   series  is  false?