Numerically Approximating LimitsSuppose that lim f(x) = L. This means that as x gets closer and closer (but notxaequal) to a, the output f(x) gets closer and closer to L. To estimate L, choose an xthat is very close to a, say, smaller than a. Then calculate f(x). Now choose anotherx that is even closer to a and smaller than a, and calculate f(x). Repeat this process.Do you notice the outputs approaching a particular number? Do the same with valuesof x that are very close to a, but greater than a. Do the outputs approach that sameparticular number? If so, you have estimated L. Otherwise, the limit does not exist.Practice9.Evaluating limx→-9 x + 9f(æ) =x+9f(x)f(x)-9.1-8.9-9.01-8.99-9.001-8.9999.?х-9 х + 9Based on the above, what do you estimate as the value for limuse decimals for all responses.• because our goal is to "get close," make sure your decimal responses areaccurate to at least 5 decimal places.• your final estimate is not expected to have as much “accuracy" - it will only be anestimate.• if the limit does not exist, enter "DNE".

The estimate value of given function is 0.5.

Answered: Evaluating lim x-9 x + 9 f(x) = 9. x+9…

Evaluating lim x-9 x + 9 f(x) = 9. x+9 f(x) f(x) -9.1 -8.9 -9.01 -8.99 -9.001 -8.999 9. ? x-9 x + 9 Based on the above, what do you estimate as the value for lim

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Numerically Approximating Limits
Suppose that lim f(x) = L. This means that as x gets closer and closer (but not
xa
equal) to a, the output f(x) gets closer and closer to L. To estimate L, choose an x
that is very close to a, say, smaller than a. Then calculate f(x). Now choose another
x that is even closer to a and smaller than a, and calculate f(x). Repeat this process.
Do you notice the outputs approaching a particular number? Do the same with values
of x that are very close to a, but greater than a. Do the outputs approach that same
particular number? If so, you have estimated L. Otherwise, the limit does not exist.
Practice
9.
Evaluating lim
x→-9 x + 9
f(æ) =
x+9
f(x)
f(x)
-9.1
-8.9
-9.01
-8.99
-9.001
-8.999
9.
?
х-9 х + 9
Based on the above, what do you estimate as the value for lim
use decimals for all responses.
• because our goal is to "get close," make sure your decimal responses are
accurate to at least 5 decimal places.
• your final estimate is not expected to have as much “accuracy" - it will only be an
estimate.
• if the limit does not exist, enter "DNE".

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