If \(\lim_{x\rightarrow 1} \frac{f(x)-6}{x-1}=5\)
evaulate \(\lim_{x\rightarrow 1} f(x)\)
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
How did you know that f(x) = 5x + 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
