calc 1 h/w
BigMo
ho5_week4homework_continuitylimitsderivativelinearization.docxMAT 136 – Homework Week #4 Name: _________________________________________
Show work clearly, completely and accurately for credit. Full credit will only be given when where all reasoning and work is provided. Please circle your final answer when appropriate.
The graph of f is given below. Use the graph to answer questions 1 and 2.
1. Find three x-values at which f is not continuous. Justify each choice using a specific reason from the definition of continuity:
a. x-value of discontinuity #1: __________ Reason for discontinuity: ________________________________
b. x-value of discontinuity #2: __________ Reason for discontinuity: ________________________________
c. x-value of discontinuity #3: __________ Reason for discontinuity: ________________________________
2. List four of the local and/or global extrema of given in problem #1.
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Local and/or Global? |
Maximum or Minimum? |
Max/Min Value? |
Max/Min Point (or interval of points)? |
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a.
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b.
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c.
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d.
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3. Where is increasing and decreasing?
4. Find the limits. Give your answers in exact form—no decimal approximations. Support your answers with appropriate work.
5a) Graph the function b) Using the limit definition of the derivative, find .
(show all work/steps thoroughly)
.
c) On your graph for part (a) draw the line tangent to the curve when
d) Find . f) Use your equation in (d) to approximate
lim x→8
x2 + x − 6 x − 8
lim
x®8
x
2
+x-6
x-8
lim x→−∞
x2 + x − 6 x − 8
lim
x®-¥
x
2
+x-6
x-8
lim x→5−
ex
x − 5( )3
lim
x®5
-
e
x
x-5
()
3
lim x→
π 2
+ etan x
lim
x®
p
2
+
e
tanx
