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Chapter 3: Q. 26 (page 314)

L鈥橦藛opital鈥檚 Rule limit calculations: Calculate each of the

limits that follow. Some of these limits are easier to calculate

by using L鈥橦opital鈥檚 rule, and some are not.

limx鈫�03x-12x-1

Short Answer

Expert verified

Limit is ln3ln2and it is easier to find using L'Hospitals rule.

Step by step solution

01

Step 1. Given information

An expression is given aslimx鈫�03x-12x-1

02

Step 2. Evaluating limit

Use properties of limit and simplify as,

limx鈫�03x-12x-1=limx鈫�03x-12x-1=limx鈫�03xln3-02xln2-0=ln3ln2limx鈫�03x2x=ln3ln2脳3020=ln3ln2

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Most popular questions from this chapter

For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.

Find the possibility graph of its derivative f'.

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

f(x)=1sinx

Use the definitions of increasing and decreasing to argue that f(x)=x4 is decreasing on (鈭�鈭�,0] and increasing on [0,鈭�). Then use derivatives to argue the same thing.

Use the definition of the derivative to find f' for each function f.

f(x)=x3+2
See all solutions

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