- #1
Seldini
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lim x->3
(x^2+1)/(x^2-4x+3)
Can anyone show me how to find the limit of this one? Thanks guys.
(x^2+1)/(x^2-4x+3)
Can anyone show me how to find the limit of this one? Thanks guys.
Seldini said:lim x->3
(x^2+1)/(x^2-4x+3)
Can anyone show me how to find the limit of this one? Thanks guys.
Parth Dave said:The limit does not exist. There are some ways you can look at this. First of all, you can just put it into a calculator and you'll see it does not exist.
Another solution is,
the number will always be positive. The denominator however will not be. You can factor it and it becomes (x - 1)(x - 3). If x is a little bit less then 3 then the denominator is negative. If x is a little greater then 3 the denominator is positive. Hence, if youre approaching from the left side, the one-sided limit is negative infinite. From the right, it is positive infinite. As you get closer and closer to 3 from either side the magnitude constant increases because the denominator gets closer and closer to zero. Hence, on either side it will constantly increase but in different directions.
Is that valid? Or is that just verbal diarrhea?
Parth Dave said:The limit does not exist. There are some ways you can look at this. First of all, you can just put it into a calculator and you'll see it does not exist.
Another solution is,
the number will always be positive. The denominator however will not be. You can factor it and it becomes (x - 1)(x - 3). If x is a little bit less then 3 then the denominator is negative. If x is a little greater then 3 the denominator is positive. Hence, if youre approaching from the left side, the one-sided limit is negative infinite. From the right, it is positive infinite. As you get closer and closer to 3 from either side the magnitude constant increases because the denominator gets closer and closer to zero. Hence, on either side it will constantly increase but in different directions.
Is that valid? Or is that just verbal diarrhea?
The limit of (x^2+1)/(x^2-4x+3) as x approaches 3 is undefined. This is because when x=3, the denominator becomes 0, which is undefined in mathematics.
To find the limit of (x^2+1)/(x^2-4x+3) as x approaches 3, we can use the direct substitution method. This means plugging in x=3 into the function and simplifying. However, since this results in an undefined value, we can also use algebraic manipulation or graphing to determine the limit.
Yes, L'Hopital's rule can be used to find the limit of (x^2+1)/(x^2-4x+3) as x approaches 3. This rule states that if the limit of the quotient of two functions is in an indeterminate form (such as 0/0 or ∞/∞), then the limit of the original function can be found by taking the derivative of the numerator and denominator and evaluating the new quotient at the given value.
Yes, the expression (x^2+1)/(x^2-4x+3) can be simplified by factoring the denominator. This results in (x^2+1)/(x-3)(x-1). However, this does not change the limit as x approaches 3. It only makes it easier to evaluate the function at that specific point.
Finding the limit of (x^2+1)/(x^2-4x+3) as x approaches 3 allows us to understand the behavior of the function near the point x=3. It tells us what value the function is approaching as x gets closer and closer to 3. This information can be useful in many mathematical and scientific applications, such as in optimization problems or in understanding the behavior of a physical system.