   Chapter 2.2, Problem 25E

Chapter
Section
Textbook Problem

Use a table of Values to estimate i:he value of the limit. If you have a graphing device. use it to confirm your result graphically. lim θ → 0 sin 3 θ tan 2 θ

To determine

To estimate: The value of limθ0sin3θtan2θ by using table of values; verify the answer graphically.

Explanation

Since θ approaches 0, the values θ=0.5,0.1,0.01,0.001,0.0001, and 0.00001 are to the left of 0 and the values θ=0.5,0.1,0.01,0.001,0.0001and 0.00001 are to the right of 0.

Evaluate the function (correct to 6 decimal places) when θ=0.5,0.1,0.01,0.001,0.0001, and 0.00001 as shown in the below table.

 θ sin3θ tan2θ f(θ)=sin3θtan2θ −0.5 −0.99749 −1.557407725 0.640484 −0.1 −0.29552 −0.202710036 1.457846 −0.01 −0.03 −0.020002667 1.499575 −0.001 −0.003 −0.002000003 1.499995 −0.0001 −0.0003 −0.0002 1.499999 −0.00001 −0.00003 −0.00002 1.5

Here, it is observed that the value of f(θ) approaches 1.5 as x closer to 0 from the left side.

That is, limθ0sin3θtan2θ=1.5.

Evaluate the function (correct to 6 decimal places) when θ=0.5,0.1,0.01,0.001,0.0001and 0.00001 as shown in the below table

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