Question
Asked Oct 26, 2019
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Please answer question a, d, e, for this function: 

 

f(x) = 1 + (1/x) - (1/x^2)

a. Find the vertical and horizontal asymptotes.
b. Find the intervals of increase or decrease.
c. Find the local maximum and minimum values.
d. Find the intervals of concavity and the inflection points.
e. Use the information from parts (a)-(d) to sketch the graph of f.
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a. Find the vertical and horizontal asymptotes. b. Find the intervals of increase or decrease. c. Find the local maximum and minimum values. d. Find the intervals of concavity and the inflection points. e. Use the information from parts (a)-(d) to sketch the graph of f.

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Expert Answer

Step 1

The given function is

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1 = 1+ 1 f(x)

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Step 2

To find:

  • The vertical and horizontal asymptotes of the function.
  • The interval of concavity and the inflection point.
  • Sketch the graph of the function using information from sub-parts (a) and (d).
Step 3
  • The function will have vertical asymptotes at those points at which denominator of the function is equal to 0.

Therefore, substitute denominator of (1) equal to 0 gives, x2 = 0, i.e. x = 0.

Hence x = 0 is the vertical asymptote of t...

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1 1 lim f(x)= lim 1+ x lim f(x) 1 1 lim f(x) lim 1+- lim f(x) 1

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Math

Calculus