Question

Consider the following.Create a table of values for the function. (Round your answers to four decimal places.)x0.90.990.9991.001 1.01 1.1f(x)Use the table to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places.)

Answer 1

we have the expression

`\lim _(x\to1)(x-8)/(x^2-4x-32)`

Create the table

For x=0.9

`f(x)=(0.9-8)/(0.9^2-4\cdot0.9-32)`

f(x)=0.2041

For x=0.99

`f(x)=(0.99-8)/(0.99^2-4\cdot0.99-32)`

f(x)=0.2004

For x=0.999

`f(x)=(0.999-8)/(0.999^2-4\cdot0.999-32)`

f(x)=0.2000

For x=1.001

`f(x)=(1.001-8)/(1.001^2-4\cdot1.001-32)`

f(x)=0.19996

For x=1.01

`f(x)=(1.01-8)/(1.01^2-4\cdot1.01-32)`

f(x)=0.1996

For x=1.1

`f(x)=(1.1-8)/(1.1^2-4\cdot1.1-32)`

f(x)=0.1961

using a graphing tool

the exact value of the limit is 0.20

the approximate value of the limit is about 0.1996