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Major Quiz 1 MA140-09: Limits and Continuity - Prof. Paula R. Stickles, Quizzes of Calculus

A major quiz for the ma140-09 course focusing on limits and continuity. It includes various limit calculations using given functions and graphs, as well as determining continuity at specific values.

Typology: Quizzes

Pre 2010

Uploaded on 08/04/2009

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koofers-user-esm 🇺🇸

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MA140-01
1/28/09
Major Quiz 1
Who are you? _______________
Show all your work and explain your answers completely. I cannot give partial credit for answers that are both
wrong and unexplained. Even correct "bottom line" answers that are mysterious and unsupported will not be
considered completely correct. Show me what you are thinking. Try to keep your answers neat and organized so th at I
can follow them easily.
1.) Find each of the following limits, if they exist.
(a)
3
214
lim
2
3
+
x
xx
x
(b)
9
62
lim
9
x
x
x
(c)
3 2
3
4 2 5
lim
8 2
x
x x
x x
→∞
+
+ +
2.)
Find k in the following function so that f(x) has a limit as x approaches 2.
( )
3 5 , 2
x x
f x x k x
=
+ >
pf3

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1/28/

Major Quiz 1 Who are you? _______________

Show all your work and explain your answers completely. I cannot give partial credit for answers that are both wrong and unexplained. Even correct "bottom line" answers that are mysterious and unsupported will not be considered completely correct. Show me what you are thinking. Try to keep your answers neat and organized so that I can follow them easily.

1.) Find each of the following limits, if they exist.

(a) 3

lim

2 (^3) −

→ (^) x

x x x

(b) 9

lim (^9) −

→ (^) x

x x

(c)

3 2

3

lim

x

x x

x x

→∞

2.) Find k in the following function so that f(x) has a limit as x approaches 2.

4 1, 2 ( ) 3 5 , 2

x x f x x k x

 +^ >

1/28/

3.) The graph of y = f(x) is given below. Use the graph to answer the following. If a limit does not exist, explain why.

(a) 5

lim ( )

x

+^ f^ x

→− (e) f(3)

(b) 1

lim ( )

x

+^ f^ x

(f)^ lim x → 3^ f^ ( ) x

(c) 1

lim ( )

x

−^ f^ x

(g) 3

lim ( )

x

f x

→−

(d) 1

lim ( )

x

f x

(h) f(1)

4.) Use the definition of continuity to determine if the function is continuous at the given value. If the function is discontinuous, state whether the discontinuity is essential or removable and why.

h(x) =

x if x if x x if x

Continuous at 1?

1

  • 1
  • 1

1