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## Homework Statement

Given that

lim

*f(x)*= 4

x → 2

lim

*g(x)*= -2

x → 2

lim

*h(x)*= 0

x → 2

find the limits that exist for the problems below. If the limits do not exist, explain why.

c)

lim √

*f(x)*

x → 2

e)

lim (

*g(x)*/

*h(x)*)

x → 2

## Homework Equations

lim √

*f(x)*

x → a

=

√(lim

*f(x)*)

x → a

and

lim (

*f(x)*/

*g(x)*)

x → a

=

(lim

*f(x)*)

x → a

/

(lim

*g(x)*)

x → a

## The Attempt at a Solution

c) Since

lim √

*f(x)*

x → 2

= 4,

√(lim

*f(x)*)

x → 2

= √4 = +2 and -2

Therefore, since 2 ≠ -2, the limit does not exist, since I don't think there can be two limits for one number.

e) Since

lim (

*f(x)*/

*g(x)*)

x → a

=

(lim

*f(x)*)

x → a

/

(lim

*g(x)*);

x → a

lim (

*g(x)*/

*h(x)*)

x → 2

=

(lim

*g(x)*)

x → 2

/

(lim

*h(x)*);

x → 2

= -2/0 = Undefined or ∞

The limit might equal +∞ or -∞ here, but since I don't actually have the function or the graph of the function to determine if the limit is +∞ or -∞, I will say the limit does not exist because division by 0 is not defined.

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