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Select the second function in "The Limit of a Function", y = Vx0.2. Use the 8-slider to find a value for 8 so that f(x) is within 0.2 of f(5) for all values of x where 5 - 8

Question

please answer parts a, b, and c 

Select the second function in "The Limit of a Function", y = Vx
0.2. Use the 8-slider to find a value for 8 so that f(x) is within 0.2 of f(5) for all values of x where 5 - 8 <x<5+ 8. What is the largest value of 8 you
(a) Set a
5 and e
can use?
0.2
X
(b) Use the graph to estimate the largest value of S so that Ix- 21 < 0.3 whenever |x - 4 < 8
1.11
(c) Zoom in at x = 3, and estimate the largest value of 8 so that x -3| < 0.01 whenever x - 3 <8.
0.2
(d) State the limit that part (c) is illustrating
limVx0.2
=
x3
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Image Transcriptionclose

Select the second function in "The Limit of a Function", y = Vx 0.2. Use the 8-slider to find a value for 8 so that f(x) is within 0.2 of f(5) for all values of x where 5 - 8 <x<5+ 8. What is the largest value of 8 you (a) Set a 5 and e can use? 0.2 X (b) Use the graph to estimate the largest value of S so that Ix- 21 < 0.3 whenever |x - 4 < 8 1.11 (c) Zoom in at x = 3, and estimate the largest value of 8 so that x -3| < 0.01 whenever x - 3 <8. 0.2 (d) State the limit that part (c) is illustrating limVx0.2 = x3

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check_circleAnswer
Step 1

To estimate the value of delta (as in epsilon - delta definition of limits) using graphing calculator

Step 2

In the solution, we assume that the grid is marked upto the tenth of a unit interval on both axes. For instance, the interval [0,1] is divided into 10 equal parts at 0,0.1,0.2 ,,,,0.9 ,1 .

Step 3

(a) the value of delta is 0.7 , under the assumption th...

(a)5 2.2, 0.2, so the y - axis
values are between 2.2 0.2 2 and
2.2+0.2 2.4
The corresponding values on the x -axis
are 22 4 and 2.42 =5.76. As 5-4
1,5.7-5=0.7,
we take 8 =0.7
help_outline

Image Transcriptionclose

(a)5 2.2, 0.2, so the y - axis values are between 2.2 0.2 2 and 2.2+0.2 2.4 The corresponding values on the x -axis are 22 4 and 2.42 =5.76. As 5-4 1,5.7-5=0.7, we take 8 =0.7

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Calculus

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