Differential and Integral Calculus by Feliciano and Uy: Limit of a Function, Exercise 1.2, Problem 1

Evaluate \lim\limits _{x\to 2}\left(x^2-4x+3\right).

SOLUTION:

\lim\limits_{x\to 2}\left(x^2-4x+3\right)=\lim \limits_{x\to 2}\left(x^2\right)-\lim\limits_{x\to 2}\left(4x\right)+\lim\limits_{x\to 2}\left(3\right)

=\left[\lim\limits _{x\to 2}\left(x\right)\right]^2-4\lim\limits _{x\to 2}\left(x\right)+3

=\left(2\right)^2-4\left(2\right)+3

=-1

 

 

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