Find the limit.
-If $\lim _ { x \rightarrow 1 } \frac { f ( x ) - 3 } { x - 1 } = 2$, find $\lim _ { x \rightarrow 1 } f ( x )$
A) 2
B) 3
C) 1
D) Does not exist

Question

Quizplus · Accepted Answer

Using the limit definition of derivative, we have f'(1) = 2. So we know that f(x) has a tangent line with slope 2 at x=1. This means that as x approaches 1, f(x) approaches a value that is 2 units above f(1). Since f(1)=3 (as given in the limit equation), we have that the limit of f(x) as x approaches 1 is equal to 3+2=5. Therefore, the answer is choice B.

Find the Limit lim⁡x→1f(x)−3x−1=2\lim _ { x \rightarrow 1 } \frac { f ( x ) - 3 } { x - 1 } = 2limx→1​x−1f(x)−3​=2

Find the Limit $\lim _ { x \rightarrow 1 } \frac { f ( x ) - 3 } { x - 1 } = 2$