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10.1

In Exercise 12, transcribe a open account restraint the succession, if undivided await, grand a lordship starting with n = 1.

12. 3, 8, 15, 24, 35, 48 ?

In Exercise 18, scold the consolidates implied.

18. ?5?=1

?

? 2 ?

In Exercise 20, ascertain the consolidate if the train converges.

2?

20. ?8

?=0 (?)

10.2

Restraint Exercises 2 and 6, ascertain the Taylor polynomial of limit n approximating the attached exercise neighboring x =

0. Using a graphing usefulness, portray the attached exercise and the Taylor access on the same

coordinate plan.

2. ? =

1

,?

1?

v

=3

6. ? = ? ln(? 1) , ? = 3

Restraint Exercise 10 and 14, ascertain the Taylor polynomial of limit n neighboring x = a restraint the attached n and a.

10. ? = evil ? , ? = ?, ? = 5

1

14. ? = ? 3 , ? = 1, ? = 4

20. Construct the Taylor polynomial of limit 3 centered at x = 2, restraint the exercise?(?) = v? 1. Use

this polynomial to prize a appraise restraintv2. Compare this to the appraise attached by your calculator.

10.3

2. Use the Taylor train restraint ex and superabundance to allure a restraintce train restraint? =

1

? ? -1

.

?

1

3. Use the Geometric train 1? = 1 ? ? 2 ? 3 ? ? ? ? to allure a restraintce train restraint 1? 2.

4. Evilce

?

arctan ?

??

?

1

= 1? 2 , we enjoy arctan ? = ?0

1

??.

1? 2

a. Substitute your rejoinder to interrogation 3 into the gross and combine account-by-term to achieve a

force train paraphrase restraint the arctangent exercise.

b. The space-between of assembly restraint the geometric train is (-1, 1). This resources the space-between of

assembly restraint the disconnection to 4a. is too expected to be (-1, 1).

However, in this plight, the space-between includes the endpoint x=1. Evilce the intention whose tangent is 1

?

?

is the intention4 , arctan(1) = 4 . Thus ? = 4 arctan (1).

Substitute x=1 into your restraintce train restraint 4(a) and achieve a numerical truthfulness restraint ? as an

infinite train (ascribable originally to Leibniz).

6.

1 1

??

1?

1 1

?0 1? ??

1 1

?0 1? ??

a. Combine ?0

using a graphing usefulness.

b. Combine

exactly.

c. Combine

by replacing the integrand with a Taylor train and combine account by account.

d. Re-wright your rejoinder to c. using consolidatemation notation and equate it to your rejoinder to segregate b.

8. In engineering, the hyperbolic evile exercise, abbreviated evilh, is defined by evilh ? =

? ? -? -?

.

2

a. Calculate the earliest immodest derivatives of evilh (t) and mention a limit 4 Taylor polynomial restraint

y=sinh (t).

b. Combine the notorious Taylor train restraint et and e-t and achieve a Taylor train restraint evilh (1). Compare your

results with segregates(a).

In quantity 24, ascertain a Taylor train polynomial of limit at smallest immodest which is a disconnection of the boundary

appraise quantity.

24. ? ‘ (?) = (1 ?)?, ?(0) = 1

10.1

In Exercise 12, transcribe a open account restraint the succession, if undivided await, grand a lordship starting with n = 1.

12. 3, 8, 15, 24, 35, 48 ?

In Exercise 18, scold the consolidates implied.

18. ?5?=1

?

? 2 ?

In Exercise 20, ascertain the consolidate if the train converges.

2?

20. ?8

?=0 (?)

10.2

Restraint Exercises 2 and 6, ascertain the Taylor polynomial of limit n approximating the attached exercise neighboring x =

0. Using a graphing usefulness, portray the attached exercise and the Taylor access on the same

coordinate plan.

2. ? =

1

,?

1?

v

=3

6. ? = ? ln(? 1) , ? = 3

Restraint Exercise 10 and 14, ascertain the Taylor polynomial of limit n neighboring x = a restraint the attached n and a.

10. ? = evil ? , ? = ?, ? = 5

1

14. ? = ? 3 , ? = 1, ? = 4

20. Construct the Taylor polynomial of limit 3 centered at x = 2, restraint the exercise?(?) = v? 1. Use

this polynomial to prize a appraise restraintv2. Compare this to the appraise attached by your calculator.

10.3

2. Use the Taylor train restraint ex and superabundance to allure a restraintce train restraint? =

1

? ? -1

.

?

1

3. Use the Geometric train 1? = 1 ? ? 2 ? 3 ? ? ? ? to allure a restraintce train restraint 1? 2.

4. Evilce

?

arctan ?

??

?

1

= 1? 2 , we enjoy arctan ? = ?0

1

??.

1? 2

a. Substitute your rejoinder to interrogation 3 into the gross and combine account-by-account to achieve a

force train paraphrase restraint the arctangent exercise.

b. The space-between of assembly restraint the geometric train is (-1, 1). This resources the space-between of

assembly restraint the disconnection to 4a. is too expected to be (-1, 1).

However, in this plight, the space-between includes the endpoint x=1. Evilce the intention whose tangent is 1

?

?

is the intention4 , arctan(1) = 4 . Thus ? = 4 arctan (1).

Substitute x=1 into your restraintce train restraint 4(a) and achieve a numerical truthfulness restraint ? as an

infinite train (ascribable originally to Leibniz).

6.

1 1

??

1?

1 1

?0 1? ??

1 1

?0 1? ??

a. Combine ?0

using a graphing usefulness.

b. Combine

exactly.

c. Combine

by replacing the integrand with a Taylor train and combine account by account.

d. Re-wright your rejoinder to c. using consolidatemation notation and equate it to your rejoinder to segregate b.

8. In engineering, the hyperbolic evile exercise, abbreviated evilh, is defined by evilh ? =

? ? -? -?

.

2

a. Calculate the earliest immodest derivatives of evilh (t) and mention a limit 4 Taylor polynomial restraint

y=sinh (t).

b. Combine the notorious Taylor train restraint et and e-t and achieve a Taylor train restraint evilh (1). Compare your

results with segregates(a).

In quantity 24, ascertain a Taylor train polynomial of limit at smallest immodest which is a disconnection of the boundary

appraise quantity.

24. ? ‘ (?) = (1 ?)?, ?(0) = 1

…

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