+0

# Calc help

0
155
3

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

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

Guest Jun 25, 2017
Sort:

#1
+79894
+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

CPhill  Jun 25, 2017
#2
0

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

Guest Jun 25, 2017
#3
+79894
+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

CPhill  Jun 25, 2017

### 7 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details