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Choose the value of k that makes the following function continuous at x=8

f(x)= {  x² - 11x + 24 / x - 8 then x < 8 

  also { -8x + k then x ≥ 8

 

I know the answer for this problem. I just need help in comprehending it. Can anyone give me a step by step walkthrough on this.

Guest Jan 30, 2015

Best Answer 

 #3
avatar+26750 
+10

What was the reasoning behind 69?  

 

82 - 11*8 + 24/8 - 8 = -29

 

-8*8 + 69 = 5

 

These aren't the same!

.

Alan  Jan 30, 2015
 #1
avatar+26750 
+10

For the function to be continuous then both parts of it must have the same value at x = 8.

 

So you must have 82 - 11*8 + 24/8 -8 = -8*8 + k or -29 = -64 + k or k = 35

.

Notice the gap when k isn't 35:

continuous and discontinuous

.

Alan  Jan 30, 2015
 #2
avatar
0

The answer I got for this problem was 69.

Guest Jan 30, 2015
 #3
avatar+26750 
+10
Best Answer

What was the reasoning behind 69?  

 

82 - 11*8 + 24/8 - 8 = -29

 

-8*8 + 69 = 5

 

These aren't the same!

.

Alan  Jan 30, 2015

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