Deck 11: Power Series

Question 1

Find the linear approximating polynomial for the function centered at a.

-f(x) = 2 + 3x - 5, a = -2

A) L(x) = -5x - 13
B) L(x) = -11x -13
C) L(x) = -11x + 3
D) L(x) = -5x + 3

Answer 1

L(x) = -5x - 13

Question 2

Find the linear approximating polynomial for the function centered at a.

-f(x) = , a = 0

A) L(x) = x - 6
B) L(x) = x + 6
C) L(x) = x - 6
D) L(x) = x + 6

Answer 2

L(x) = x + 6

Question 3

Find the linear approximating polynomial for the function centered at a.

-f(x) = , a = 0

A) L(x) = x +
B) L(x) = - x +
C)L(x) = x -
D) L(x) = - x -

Answer 3

L(x) = - x -

Question 4

Find the linear approximating polynomial for the function centered at a.

-f(x) = , a = 0

A)L(x) = x
B) L(x) = x
C) L(x) = - x
D) L(x) = - x

Question 5

Find the linear approximating polynomial for the function centered at a.

-f(x) = x + , a = 4

A) L(x) = x +
B) L(x) = x +
C) L(x) = x +
D) L(x) = x +

Question 6

Find the linear approximating polynomial for the function centered at a.

-f(x) = , a = 8

A) L(x) = x +
B) L(x) = x +
C) L(x) = x +
D) L(x) = x + 4

Question 7

Find the linear approximating polynomial for the function centered at a.

-f(x) = tan x, a = $\pi$

A) L(x) = x -2 $\pi$
B) L(x) = x + $\pi$
C) L(x) = x - $\pi$
D) L(x) = 2x - $\pi$

Question 8

Find the linear approximating polynomial for the function centered at a.

-f(x) = tan x, a = 0

A) L(x) = 0
B) L(x) = 5x + 1
C) L(x) = x
D) L(x) = -x

Question 9

Find the quadratic approximation of f at x = 0.

-f(x) = 2x

A) Q(x) = 1 - 2
B) Q(x) = 2x
C) Q(x) = 1 + 2
D) Q(x) 1 + 1

Question 10

Find the quadratic approximation of f at x = 0.

-f(x) = tan 7x

A) Q(x) = 1 -
B) Q(x) = 7x
C) Q(x) = 1 +
D) Q(x) = 1 + 7

Question 11

Find the quadratic approximation of f at x = 0.

-f(x) =

A) Q(x) = 3 -
B) Q(x) = 3 -
C) Q(x) = 3 +
D) Q(x) = 3 +

Question 12

Find the quadratic approximation of f at x = 0.

-f(x) = ln(cos 2x)

A) Q(x) = 2
B) Q(x) = -2
C) Q(x) = 1 + 2
D) Q(x) = 1 - 2

Question 13

Find the quadratic approximation of f at x = 0.

-f(x) = ln(1 + sin 10x)

A) Q(x) = 1 - 10x + 50
B) Q(x) = 10x + 50
C) Q(x) = 10x - 50
D) Q(x) = 1 + 10x + 50

Question 14

Find the quadratic approximation of f at x = 0.

-f(x) =

A) Q(x) = 1 + 9x +
B) Q(x) = 9x -
C) Q(x) = 1 - 9x +
D) Q(x) = 9x +

Question 15

Find the quadratic approximation of f at x = 0.

-f(x) =

A) Q(x) = 5x +
B) Q(x) = 1 + 5x +
C) Q(x) = 5x
D) Q(x) = 5x -

Question 16

Find the quadratic approximation of f at x = 0.

-f(x) = x

A) Q(x) = 4
B) Q(x) = 1 - 2x
C) Q(x) = 2x
D) Q(x) = 1 + 2x

Question 17

Find the quadratic approximation of f at x = 0.

-f(x) =

A) Q(x) = 4x
B) Q(x) = 1 +
C) Q(x) =
D)Q(x) = 1 + 4x

Question 18

Find the quadratic approximation of f at x = 0.

-f(x) = sin ln( 2x + 1)

A) Q(x) = 1 + 2x + 2
B) Q(x) = 2x - 2
C) Q(x) = 2x + 2
D) Q(x) = 1 - 2x + 2

Question 19

Find the Taylor polynomial of order 3 centered at 0.

-f(x) =

A) (x) = + + +
B) (x) = - + -
C) (x) = - + -
D) (x) = + + +

Question 20

Find the Taylor polynomial of order 3 centered at 0.

-f(x) =

A) (x) = - + -
B) (x) = + + +
C) (x) = - + -
D) (x) = + + +

Question 21

Find the Taylor polynomial of order 3 centered at 0.

-f(x) =

A) (x) = 1 - 9x + -
B) (x) = 1 - 81x + -
C) (x) = 1 - 9x + -
D) (x) = 1 - 9x + -

Question 22

Find the Taylor polynomial of order 3 generated by f at a.

-f(x) = , a = 1

A) (x) = - + -
B) (x) = - + -
C) (x) = - + -
D) (x) = - + -

Question 23

Find the Taylor polynomial of order 3 generated by f at a.

-f(x) = , a = 1

A) (x) = - + -
B) (x) = - + -
C) (x) = - + -
D)

Question 24

Find the Taylor polynomial of order 3 generated by f at a.

-f(x) = ln x, a = 3

A) (x) = - + -
B) (x) = + + +
C) (x) = ln 3 - + -
D) (x) = ln 3 + - +

Question 25

Find the Taylor polynomial of order 3 generated by f at a.

-f(x) = ln(x + 1), a = 5

A) (x) = ln 6 - + -
B) (x) = ln 4 - + -
C) (x) = ln 4 + + +
D) (x) = ln 6 + - +

Question 26

Find the Taylor polynomial of order 3 generated by f at a.

-f(x) = , a = 3

A) (x) = 1 + 18(x - 3) + 81 + 324
B) (x) = 1 + 6(x - 3) + 9 + 12
C) (x) = 9 + 6(x - 3) +
D) (x) = 9 + 6(x - 3) + 9 + 12

Question 27

Find the Taylor polynomial of order 3 generated by f at a.

-f(x) = , a = 7

A) (x) = 6 + 3(x - 7) + +
B) (x) = 1372 + 147(x - 7) + 14 +
C) (x) = 343 + 147(x - 7) + 21 +
D) (x) = 343 + 49(x - 7) + 49 +

Question 28

Find the Taylor polynomial of order 3 generated by f at a.

-f(x) = + x + 1, a = 4

A) (x) = 5 + 9(x - 4) + 13
B) (x) = 1 + 3(x - 4) + 3 +
C) (x) = 21 + 9(x - 4) +
D) (x) = 21 + 9(x - 4) + 9 + 21

Question 29

Find the series' radius of convergence.

-

A) $\infty$ , for all x
B) 2
C) 1
D) 0

Question 30

Find the series' radius of convergence.

-

A) 0
B) 1
C) $\infty$ , for all x
D) 2

Question 31

Find the series' radius of convergence.

-

A) 2
B) $\infty$ , for all x
C) 0
D) 1

Question 32

Find the series' radius of convergence.

-

A) 8
B) 4
C) 0
D) $\infty$ , for all x

Question 33

Find the series' radius of convergence.

-

A) 0
B) $\infty$ , for all x
C) 2
D) 1

Question 34

Find the series' radius of convergence.

-

A) 2
B) 0
C) $\infty$ , for all x
D) 1

Question 35

Find the series' radius of convergence.

-

A) 1
B) $\infty$ , for all x
C) 5
D) 10

Question 36

Find the series' radius of convergence.

-

A) $\infty$ , for all x
B) 4
C) 2
D) 1

Question 37

Find the series' radius of convergence.

-

A) $\infty$ , for all x
B) 2
C) 1
D) 0

Question 38

Determine the radius of convergence of the power series.

-

A) $\infty$
B) 1
C)
D) 4

Question 39

Determine the radius of convergence of the power series.

-

A) 4
B) 0
C) 8
D) $\infty$

Question 40

Find the interval of convergence of the series.

-

A) -3 < x < 3
B) 1 $\le$ x < 3
C) 1 < x < 3
D) x < 3

Question 41

Find the interval of convergence of the series.

-

A) x < 9
B) 7 $\le$ x < 9
C) 2 $\le$ x < 14
D) 7 < x < 9

Question 42

Find the interval of convergence of the series.

-

A) 1 < x < 9
B) -1 $\le$ x $\le$ 11
C) 4 $\le$ x < 6
D) -1 < x < 11

Question 43

Find the interval of convergence of the series.

-

A) -16 < x < 16
B) 7 $\le$ x $\le$ 9
C) x < 16
D) 0 $\le$ x $\le$ 16

Question 44

Find the interval of convergence of the series.

-

A) 2 $\le$ x < 4
B) - $\infty$ < x < $\infty$
C) 2 < x < 4
D) x < 4

Question 45

Find the interval of convergence of the series.

-

A) x $\le$ 5
B) 3 $\le$ x $\le$ 5
C) - $\infty$ < x < $\infty$
D) -116 $\le$ x $\le$ 124

Question 46

Find the interval of convergence of the series.

-

A) x < 12
B) 6 < x < 8
C)-12 < x < 12
D) 2 < x < 12

Question 47

Determine the interval of convergence of the power series.

-

A) (-6, 4)
B)
C) (- $\infty$ , $\infty$ )
D) (-5, 5)

Question 48

Determine the interval of convergence of the power series.

-

A)
B) (-4, 4)
C) (- $\infty$ , $\infty$ )
D) x = 0

Question 49

Find the function represented by the power series.

-

A)

B)
-
C)

D)
-

Question 50

Find the function represented by the power series.

-

A)
-
B)

C)
-
D)

Question 51

Find the function represented by the power series.

-

A)
B) -
C)
D) -

Question 52

Find the function represented by the power series.

-

A) -
B) -
C) -
D)-

Question 53

Find the function represented by the power series.

-

A)
B) -
C)
D)-

Question 54

Find the function represented by the power series.

-

A) -
B)
C)
D) -

Question 55

Find the first four nonzero terms in the Maclaurin series for the function.

-f(x) =

A) 1 + 4x + + + . . .
B) 1 + 4x + + + . . .
C) x + 4x + + + . . .
D) 4x + 64 + 1024 + 16,384 + . . .

Question 56

Find the first four nonzero terms in the Maclaurin series for the function.

-f(x) =

A)

B)

C)

D)

Question 57

Find the first four nonzero terms in the Maclaurin series for the function.

-f(x) = ln (1 + )

A)

B)

C)

D)

Question 58

Find the first four nonzero terms in the Maclaurin series for the function.

-f(x) = x sin( 3x)

A)

B)

C)

D)

Question 59

Find the first four nonzero terms in the Maclaurin series for the function.

-f(x) = sin x cos x

A)

B)

C)

D)

Question 60

Find the Taylor series generated by f at x = a.

-f(x) = 8x + 2, a = 2

A) 8(x - 2) + 14
B) 8(x - 2) + 18
C) 8(x + 2) + 18
D) 8(x + 2) + 14

Question 61

Find the Taylor series generated by f at x = a.

-f(x) = - 10x - 8, a = 3

A) - 4(x + 3) - 13
B) - 4(x - 3) - 29
C) - 4(x - 3) - 13
D) - 4(x + 3) - 29

Question 62

Find the Taylor series generated by f at x = a.

-f(x) = + 9 + 9x - 4, a = 5

A)
B)
C)
D)

Question 63

Find the Taylor series generated by f at x = a.

-f(x) = - 4 + 3x + 5, a = 5

A)
B)
C)
D)

Question 64

Find the Taylor series generated by f at x = a.

-f(x) = , a = 10

A)

B)

C)

D)

Question 65

Find the Taylor series generated by f at x = a.

-f(x) = , a = 7

A)

B)

C)

D)

Question 66

Find the Taylor series generated by f at x = a.

-f(x) = , a = 2

A)

B)

C)

D)

Question 67

Find the Taylor series generated by f at x = a.

-f(x) = , a = 7

A)

B)

C)

D)

Question 68

Find the Taylor series generated by f at x = a.

-f(x) = , a = 10

A)

B)

C)

D)

Question 69

Find the Taylor series generated by f at x = a.

-f(x) = , a = 4

A)

B)

C)

D)

Question 70

Use power series operations to find the Taylor series at x = 0 for the given function.

-f(x) =

A)

B)

C)

D)

Question 71

Use power series operations to find the Taylor series at x = 0 for the given function.

-f(x) =

A)

B)

C)

D)

Question 72

Use power series operations to find the Taylor series at x = 0 for the given function.

-f(x) = sin x

A)

B)

C)

D)

Question 73

Use power series operations to find the Taylor series at x = 0 for the given function.

-f(x) = cos $\pi$ x

A)

B)

C)

D)

Question 74

Use power series operations to find the Taylor series at x = 0 for the given function.

-f(x) = ( 4x)

A)
+
B)
+
C)
+
D)
+

Question 75

Use power series operations to find the Taylor series at x = 0 for the given function.

-f(x) =

A)

B)

C)

D)

Question 76

Use power series operations to find the Taylor series at x = 0 for the given function.

-f(x) =

A)

B)

C)

D)

Question 77

Use power series operations to find the Taylor series at x = 0 for the given function.

-f(x) = ln(1 + 4x)

A)

B)

C)

D)

Question 78

Use power series operations to find the Taylor series at x = 0 for the given function.

-f(x) = ( 8x)

A)

B)

C)

D)

Question 79

Use power series operations to find the Taylor series at x = 0 for the given function.

-f(x) =

A)

B)

C)

D)

Question 80

Find the first four terms of the binomial series for the given function.

-

A)

B)

C)

D)