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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
avatar+98061 
+1

 

 

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

 

 

 

 

cool cool cool

 May 15, 2018
 #2
avatar+98061 
+1

2. lim x -> 0 

sin ( 1/x  )

 

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

 

https://www.desmos.com/calculator/apbhkqpybo

 

 

 

cool smileycool

 May 15, 2018
 #3
avatar+98061 
+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

 

 

cool cool cool

 May 15, 2018

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