If the limit as x approaches 1 for (f(x) - 7)/(x-1)=8,
evaluate the limit as x approaches 1 for f(x)
the left is undefined as x >> 1
but for any other x very close to x = 1
f(x) - 7 = 8(x-1)
for example if x = .99
f(.99) - 7 = 8(.99-1) = 8 (-.01) = - .08
f(.99) = 7 -.08
which might give us a hint as to where f(x) was going :)
in fact it looks to me like
f(x) - 7 = 8(x-1)
is similar to
f(x) = 7 + 8(x-1)
and as x >>1
f(1) =7 +8(0) = 7
Thank you so much!!
To evaluate the limit as x approaches 1 for f(x), we need to use algebraic manipulation to isolate f(x) in the given equation.
Given: (f(x) - 7)/(x-1) = 8
Multiplying both sides by (x-1), we get:
f(x) - 7 = 8(x-1)
Simplifying the equation:
f(x) - 7 = 8x - 8
Adding 7 to both sides:
f(x) = 8x - 8 + 7
Simplifying further:
f(x) = 8x - 1
Now that we have isolated f(x), we can evaluate the limit as x approaches 1 by substituting x = 1 into the equation:
f(1) = 8(1) - 1
Simplifying the expression:
f(1) = 8 - 1
f(1) = 7
Therefore, the limit as x approaches 1 for f(x) is 7.
To evaluate the limit as x approaches 1 for f(x), we need to manipulate the given equation and solve for f(x).
Given equation:
(f(x) - 7)/(x - 1) = 8
To isolate f(x), we can multiply both sides of the equation by (x - 1):
(f(x) - 7) = 8(x - 1)
Next, distribute 8 on the right side of the equation:
f(x) - 7 = 8x - 8
Now, isolate f(x) by adding 7 to both sides of the equation:
f(x) = 8x - 8 + 7
Simplifying the right side gives:
f(x) = 8x - 1
Now we have an equation for f(x):
f(x) = 8x - 1
To evaluate the limit as x approaches 1 for f(x), we substitute 1 into this equation:
f(1) = 8(1) - 1
f(1) = 8 - 1
f(1) = 7
Therefore, the limit as x approaches 1 for f(x) is 7.