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Calc 1 1.5

 

<== Calculus 1
Number Question Answer
See the work

4.

 

Let 

Show that f(x) has a jump discontinuity at x= 5 by calculating
the limits from the left and right at x= 5.

 

12

0.14285714286

The work

Point Cost: 1

5.

 

Let 

Find the indicated one-sided limits of f , and determine the
continuity of f at the indicated point.

ƒ(-3)=________

Is ƒ continuous at x= -3?

 

3

8

DNE

8

No

The work

Point Cost: 1

6.

 

Let

Find the indicated one-sided limits of ƒ, and determine the
continuity of ƒ at the indicated point.


ƒ(7)=_________

Is ƒ continuous at x=7 ________

 

-14

14

DNE

ƒ(7)= 1

Not continuous at 7 

 

The work

Point Cost: 1

7.

 

Let


ƒ(x)=(x-8)/((x-1)(x+3))


use interval notation to indicate where ƒ(x) is continuous.

 

(-∞, -3) U (-3,1) U (1, ∞) 
The work

Point Cost: 2

8.

 

Let


ƒ(x)=7x^8-4x^4+2


use interval notation to indicate where ƒ(x) is continuous.

 

(-∞, ∞) The work

9.

 

Let


ƒ(x)=sqrt(x-3)


use interval notation to indicate where ƒ(x) is continuous.

 

[3, ∞)
The work

Point Cost: 1

10.

 

Let


ƒ(x)=(x-2)^(1/3)


use interval notation to indicate where ƒ(x) is continuous.

 

(-∞, ∞) The work

11.

 

For what value of the constant c is the function ƒ 
continuous on (-∞, ∞) where

 c=______

 

34/7
The work

Point Cost: 3

12.

 

Let

Show that ƒ(x) has a removable discontinuity at x= -4 and
determine what value for ƒ(-4) would make ƒ(x) continuous at
x= -4.
Must redefine ƒ(-4)=______

 

ƒ(-4)=2
The work

Point Cost: 1

13.

 

Let

Show that ƒ(x) has a jump discontinuity at x= 3 by calculating 
the limits from the left and right at x=3

 

21

-14

The work

Point Cost: 1

14.

 

Determine if the Intermediate Value Theorem implies
that the equation x^3-3x-1.9=0 has a root in the interval
(0,1).

 

No

 

The work

15.

 

Let ƒ be a continuous function such that
ƒ(-6)=-1 and ƒ(6)= 1.
Using the Intermediate Value Theorem classify
the following statements as
( A ) Always true
( B ) Never True, or
( C ) True in some cases; False in others.
1. ƒ(0)= 0
Answer:___
2. For some c , where -6 &le c &le 6, ƒ(c)= 0.
Answer:___
1. C
2. A
The work