Calculus Volume 1

Chapter 2 | Limits

151

f ( x ); lim

f ( x ); lim

f ( x ); f (−2)

lim x →−2 −

b.

x →−2

x →−2 +

f ( x ); lim

f ( x ); lim x →1 f ( x ); lim x →3

f ( x ); f (1)

lim x →1 − lim x →3 −

c.

x →1 +

f ( x ); lim

f ( x ); f (3)

d.

x →3 +

Figure 2.21 The graph shows f ( x ).

Solution Using Infinite Limits from Positive Integers and the graph for reference, we arrive at the following values: a. lim x →−4 − f ( x ) =0; lim x →−4 + f ( x ) =0; lim x →−4 f ( x ) =0; f (−4) =0 b. lim x →−2 − f ( x ) =3.; lim x →−2 + f ( x ) =3; lim x →−2 f ( x ) =3; f (−2) is undefined c. lim x →1 − f ( x ) =6; lim x →1 + f ( x ) =3; lim x →1 f ( x ) DNE; f (1) =6 d. lim x →3 − f ( x ) =−∞; lim x →3 + f ( x ) =−∞; lim x →3 f ( x ) =−∞; f (3) is undefined

f ( x ) for f ( x ) shown here:

Evaluate lim x →1

2.10

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