If lim x→1 f(x) − 9x − 1 = 8, find lim x→1 f(x).
Question
If lim x→1 f(x) − 9x − 1 = 8, find lim x→1 f(x).
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Solution
To find the limit as x approaches 1 of f(x), we can rearrange the given equation.
We know that lim (x→1) [f(x) - 9x - 1] = 8.
We can rewrite this as: lim (x→1) f(x) = 8 + lim (x→1) [9x + 1].
As x approaches 1, 9x + 1 becomes 9(1) + 1 = 10.
So, lim (x→1) f(x) = 8 + 10 = 18.
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