If lim x->4 f(x)-5/x-2 =1, find
lim x->4 f(x).
I know the answer is 7, I need help on solving it.
Thanks
well, just plug in x=4!
(f(4)-5)/(4-2) = 1
f(4)-5 = 2
f(4) = 7
In the absence of anything to indicate that f(x) is not continuous, I assume that
lim(x->4) f(x) = f(4)
To find the value of lim x->4 f(x), we can use algebraic manipulation and substitution.
Given that lim x->4 (f(x)-5)/(x-2) = 1, we can simplify the expression by multiplying both sides of the equation by (x-2):
lim x->4 (f(x)-5)/(x-2) * (x-2) = 1 * (x-2)
This simplifies to:
lim x->4 f(x) - 5 = x - 2
Now, we can rearrange the equation to isolate lim x->4 f(x):
lim x->4 f(x) = x - 2 + 5
Substituting the value x = 4, we get:
lim x->4 f(x) = 4 - 2 + 5 = 7
Therefore, the limit of f(x) as x approaches 4 is 7.