Question

A graphing calculator is recommended.

For the limit

lim x → 2 (x³ − 3x + 8) = 10

illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (Round your answers to four decimal places.)

ε = 0.2	δ =
ε = 0.1	δ =

Answer 1

• The largest possible value of delta can we taken as such that .
• At f(x) have value f(x)=10.2 or f(x)=9.8 .
• From the graph the value of x at f(x)=10.2 is 2.0219 and x=1.9774 at f(x)=9.8 and from this data for we get the value of 0.0219.
• At f(x) have value f(x)=10.1 or f(x)=9.9 .
• Similarly for the the value of x at f(x)=10.1 is x=2.011 and at f(x)=9.9 have x=1.9888 from this data and the figure we get the value of
• In figure in red f(x) is drawn near x=2. The blue line corresponds to and black corresponds to and in green the x=2 line is shown.
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