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Precalc

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Find the following limits if they exist

1. Iim x -> 4

(1)/(x-4)

2. lim x -> 0

sin 1/x

3. lim x -> 1 f(x) if f(x) {x+2 if x = 1, 2x2-1 if x >1

4. Consider f(x) = (x+3)/(|x+3|)

a. lim x -> -3f(x) =

b. lim x -> -3f(x) =

c. lim x -> -3 f(x) =

May 15, 2018

#1
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1. Iim x -> 4

(1)/(x-4)

This limit will not exist.....as x  approaches 4 from the left  the function becomes increasingly more negative......as  x  approaches 4 from the right, the function becomes increasingly more positive

Here's a graph to show this  :

https://www.desmos.com/calculator/sxf0xscp3a   May 15, 2018
#2
+1

2. lim x -> 0

sin ( 1/x  )

This limit does not exist  ....see  the graph here :

https://www.desmos.com/calculator/apbhkqpybo   May 15, 2018
#3
+1

3. lim x -> 1 f(x) if f(x) {x+2 if x = 1, 2x^2 - 1 if x >1

When x approaches  1 from the left, f(x)  = (1) + 2  = 3

When x  approaches 1 from the right, f(x)  = 2(1)^2  - 1  =  1

So.....this limit  does not exist as  x approaches 1 because both limits would have to be the same approaching from the left and the right   May 15, 2018