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Chapter 1: 2P (page 17)

In the following problems, find the limit of the given sequence asn→∞

Short Answer

Expert verified

The limit of the expressionis 12

Step by step solution

01

Definition of limits

A limit of a function/expression/sequence is used when the value of the function/sequence cannot be calculated directly or is difficult to calculate at a particular value. It is generally defined as the output obtained when the input is very close to the input value

01

Given parameters

The given expression isand the limit is n→∞

01

Solve the limits

Open the parentheses using the formula

Divide the numerator and denominator of the obtained expression by n2

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Most popular questions from this chapter

Use Maclaurin series to evaluate each of the following. Although you could do them by computer, you can probably do them in your head faster than you can type them into the computer. So use these to practice quick and skillful use of basic series to make simple calculations.

d10dx10(x8tan2x)atx=0.

∫0xsintdtt

Find the sum of each of the following series by recognizing it as the Maclaurin series for a function evaluated at a point ∑n=1∞1n2n.

Find the sum of each of the following series by recognizing it as the Maclaurin series for a function evaluated at a point ∑n=0∞(-12n)(-12)n.

Use Maclaurin series to evaluate each of the following. Although you could do them by computer, you can probably do them in your head faster than you can type them into the computer. So use these to practice quick and skillful use of basic series to make simple calculations.

limx→0tanx-xx3.

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