Question:
$\lim_{x \to 2} \frac {2x^2-5x+2} {x^2 -3x +2} $
$\lim_{x \to 2} \frac {2x^2-5x+2} {x^2 -3x +2} $
Updated On: Jul 6, 2022
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The Correct Option is C
Solution and Explanation
$\lim_{x\to2} \frac{2x^{2}-5x +2}{x^{2}-3x +2} = \lim_{x\to2} \frac{\left(x-2\right)\left(2x-1\right)}{\left(x-2\right)\left(x-1\right)} $
$\lim_{x\to2} \frac{2x-1}{x-1}=\frac{4-1}{2-1}=3$
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Concepts Used:
Limits
A function's limit is a number that a function reaches when its independent variable comes to a certain value. The value (say a) to which the function f(x) approaches casually as the independent variable x approaches casually a given value "A" denoted as f(x) = A.
If limx→a- f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the left of ‘a’. This value is also called the left-hand limit of ‘f’ at a.
If limx→a+ f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the right of ‘a’. This value is also called the right-hand limit of f(x) at a.
If the right-hand and left-hand limits concur, then it is referred to as a common value as the limit of f(x) at x = a and denote it by lim x→a f(x).