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Fill in the blanks to complete each of the following theorem statements.

Basic Limit Rules for Convergent Sequences: If akandbkareconvergentsequenceswithakLandbkMaskand if c is any constant, then

If f is a function that is _____ at L, thenf(ak)

Short Answer

Expert verified

The required answer is f is a function that is continuous at L, thenf(ak)f(L)

Step by step solution

01

Step 1. Given Information  

The given data is ifakandbkareconvergentsequenceswithakLandbkMask

02

Step 2. Explanation   

Using the concept of limits of functions of sequences, that is,

If akLand f is a function that is continuous at L thenf(ak)f(L)

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Most popular questions from this chapter

Prove that if k=1akconverges to L and k=1bkconverges to M , then the seriesk=1ak+bk=L+M.

Improper Integrals: Determine whether the following improper integrals converge or diverge.

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Leila finds that there are more factors affecting the number of salmon that return to Redfish Lake than the dams: There are good years and bad years. These happen at random, but they are more or less cyclical, so she models the number of fish qkreturning each year as qk+1=(0.14(1)k+0.36)(qk+h), where h is the number of fish whose spawn she releases from the hatchery annually.

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