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If   \(\lim_{x\rightarrow 1} \frac{f(x)-6}{x-1}=5\)

 

evaulate  \(\lim_{x\rightarrow 1} f(x)\)

Guest Jun 25, 2017
 #1
avatar+87334 
+1

 

 

Notice  that  if f(x)   = 5x + 1, we have that

 

 

lim              [ 5x + 1]  - 6                        5x   - 5                5 (x - 1)

                 __________         =             ______       =      ______        =   5

x → 1            x - 1                                    x  -  1                  x  - 1

 

 

So

 

lim          5x  +  1        =  5(1)  + 1    =    6

x → 1

 

 

 

cool cool cool

CPhill  Jun 25, 2017
 #2
avatar
0

How did you know that f(x) = 5x + 1 ?

Guest Jun 25, 2017
 #3
avatar+87334 
+1

 

We can solve this to find f(x)

 

[f(x)  -  6]  /  (x - 1)   =  5        multiply both sides by x - 1

 

f(x)  -  6   =  5(x  - 1)            simplify

 

f(x)   -  6   = 5x  - 5            add 6 to both sides

 

f(x)  =  5x  +  1

 

 

cool cool cool

CPhill  Jun 25, 2017

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