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```							Section 5.1 - Limits

No Calculator
Limit – the limit tells THE INTENDED HEIGHT of f(x) as x
approaches a particular value ‘c’ from BOTH directions.
lim f  x   L
x c

lim f  x   2
x 0

lim f  x   DNE
x 2

lim f  x   0
x 1

lim f  x   DNE
x 1

lim f  x   DNE
x 2
New Graph…try these five limits

lim f  x   DNE
x 2

lim f  x   0
x 1

lim f  x   2
x 0

lim f  x   DNE
x 1

lim f  x   DNE
x 2
lim f  x   1   lim f  x   1
x 2                x 2

lim f  x        lim f  x   
x 1                x 1

lim f  x   1      lim f  x   1
x 0                 x 0

lim f  x   2    lim f  x   2
x 1                 x 1

lim f  x   2    lim f  x   3
x 2                 x 2

lim f  x   1    lim f  x   1
lim f  x   DNE lim f  x   1     x 3                 x 3
x 5                x 5
lim f  x   1    lim f  x   1
lim f  x   2      lim f  x   2    x4                  x4
x 4                x 4
lim f  x   1     lim f  x   DNE
lim f  x      lim f  x      x 5                 x 5
x 3                x 3
Evaluation by Substitution

lim  5x   5  4   20
x4

lim  x  3    3  3   36
2            2

x 3

lim  3x  1   3  1  1  4
x 1

lim 10  3x   10  3 12   26
x 12

                      
lim x  2x  4x  8   2   2  2   4  2   8  32
x  2
3   2                        3           2

4      4
lim
x 5 x  7
      2
57
x2               2  2     4 1
lim 2                               
x 2 x  5x  6
 2  5  2  6 20 5
2

x2                    x2              1   1   1
lim 2             lim                              
x  2 x  5x  6   x  2  x  3  x  2 
x 3 23 5

x3                     x3                      1        1     1
lim                  lim                       lim                    
x  3 x 2  4x  3   x  3  x  1 x  3    x  3  x  1   3  1 2

lim
x 2  3x  2
 lim
 x  1 x  2          x  2   1
lim
x  1 x 2  x  2   x  1  x  1 x  2    x 1  x  2    3
x 5               x 5                    1        1
lim 2       lim                     lim           
x 5 x  25   x 5  x  5  x  5    x 5  x  5    10

x 2                   x 2                            1      1
lim       lim                                lim            
x4  x4    x 4
   x 2      x 2        x 4
   x 2  4

x     x 1
lim               1
1  x x  1

x 1

```
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