# True and False Practice – Chapter 2

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```					True and False Practice – Chapter 2

 2x        8             2x             8
1)           x  4  x  4   xlim4 x  4  xlim4 x  4 .
lim                
x4                                     
               

x 2  6x  7   lim x 2  6 x  7
x 1
2)      lim                =                   .
x  1 x 2  5x  6   lim x 2  5 x  6
x 1

x3                   lim x  3
x 1
3)      lim               =                              .
x 1   x  2x  4
2
lim x 2  2 x  4
x 1

4)      If lim f ( x)  2 and lim g ( x)  0 , then lim [ f ( x) / g ( x) ] does not exist.
x 5                     x 5                        x 5

5)      If lim f ( x)  0 and lim g ( x)  0 , then lim [ f ( x) / g ( x) ] does not exist.
x 5                     x 5                        x 5

6)      If lim [ f ( x) g ( x) ] exists, then the limit must be f (6) g (6) .
x 6

7)      If p is a polynomial, then lim p( x)  p ( b )
x b

8)      If lim f ( x)   and lim g ( x)   then the lim [ f ( x)  g ( x)]  0 .
x 0                  x 0                                x 0

9)      A function can have two horizontal asymptotes.

10)     If f has domain [ 0 ,  ) and has no horizontal asymptote, then         lim f ( x)   or
x

lim f ( x)    .
x

T/F Practice – C2
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11)   If the line x = 1 is a vertical asymptote of y = f(x), then f is not defined at 1.

12)   If f (1)  0 and       f ( 3)  0 , then there exists a number c between 1 and 3 such that f(c) = 0.

13)   If f is continuous at 5 and f ( 5) = 2 and f (4) = 3, then lim f (4 x 2  11)  2
x 2

14)   If f is continuous on [ -1, 1 ] and f (-1 ) = 4 and f (1 ) = – 3, then there exists a number r such
that | r | < 1 and f (r ) = 

15)   Let f be a function such that lim f ( x)  6 . Then there exists a number  such that if
x 0

0  | x |   then | f ( x )  6 |  1 .

16)   If f ( x )  1 for all x and lim f ( x)       exists, then lim f ( x)  1 .
x 0                           x 0

17)   If f is continuous at a , then f is differentiable at a.

18)   If f ' ( r ) exists, then lim f ( x)  f ( r ) .
x r

2
d2 y    dy 
19)          
 dx 
2
dx

20)   The equation x10 – 10 x 2 + 5 = 0 has a root in the interval ( 0, 1 )

T/F Practice – C2
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