Draw the graph of the function. YOU DON\'T HAVE TO DRAW THE GRAPH JUST ANSWER a,

Question

Draw the graph of the function. YOU DON'T HAVE TO DRAW THE GRAPH JUST ANSWER a,b,c, d, and e PLEASE!
y = f(x) = 5/x
between
x = 1/2
and
x = 4.


Find the slope of the line between the following points.
(a)
x = 3 and x = 3.1





(b)
x = 3 and x = 3.01



(c)
x = 3 and x = 3.001



(d) Now use algebra to find a simplified rational expression for the slope of the line between
(3, f(3))
and
(3 + h, f(3 + h)),

(h ? 0).
(Simplify your answer completely.)______________


(e) What do these slopes tend toward as h is made closer and closer to 0?_________

Explanation / Answer

f(x) = 5/x
a f(3) = 5/3
f(3.1) = 5/3.1
The slope from (3, 5/3) to (3.1, 5/3.1) =

(5/3.1 - 5/3)/(3.1-3) =
5(1/3.1 - 1/3)/(3.1-3)
5(3 - 3.1)/(3.1(3))/(3.1-3) =
-5/(3.1(3)) = -5/9.3 = -50/93 -0.537634408602151

b)f(3.01) = 5/3.01
The slope from (3, 5/3) to (3.01, 5/3.01) =

(5/3.01 - 5/3)/(3.01-3) =
5(1/3.01 - 1/3)/(3.01-3)
5(3 - 3.01)/(3.01(3))/(3.01-3) =
-5/(3.01(3)) = -5/9.03 = -500/903 -0.553709856035437

c)f(3.001) = 5/3.001
The slope from (3, 5/3) to (3.001, 5/3.001) =

(5/3.001 - 5/3)/(3.001-3) =
5(1/3.001 - 1/3)/(3.001-3)
5(3 - 3.001)/(3.001(3))/(3.001-3) =
-5/(3.001(3)) = -5/9.003 = -5000/9003 -0.555370432078196

d) f(3+h) = 5/(3+h)

The slope from (3, 5/3) to (3+h,5/(3+h) ) =

(5/(3+h) - 5/3)/(3+h - 3) =

5(1/(3+h) - 1/3)/h =

5(3 - (3+h))/((3+h)3)/h =

5(-h)/(9+3h)/h =

-5/(9+3h)

e) As h goes to 0, 9 + 3h goes to 9, and -5/(9+3h) goes to -5/9 -.555555555555556

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