How do you find the limit #lim_(x->2)(x^2+x-6)/(x-2)# ?
Start by factoring the numerator:
We can see that the It should now be easy to see what the limit evaluates to: Let's take a look at a graph of what this function would look like, to see if our answer agrees:
The "hole" at And, when
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To find the limit of the given expression, we can directly substitute the value of x into the expression. However, since the expression is undefined when x = 2, we need to use algebraic manipulation to simplify it. By factoring the numerator, we get (x-2)(x+3). Canceling out the common factor of (x-2) in the numerator and denominator, we are left with the limit as x approaches 2 of (x+3). Substituting x = 2 into this expression, we find that the limit is equal to 5.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you prove that the limit of #(x^3 - 3) = 5# as x approaches 2 using the epsilon delta proof?
- How do you evaluate # ((x^2)-x-6)/(x-3)# as x approaches 3?
- What is the limit of #x^2e^x# as x goes to infinity?
- How do you evaluate the limit #((2y^2+2y+4)/(6y-3))^(1/3)# as y approaches 5?
- How do you find the limit of #(x+3)^2# as #x->-4#?

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