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[Miwaa]

evaluate limx---3 (x^2 +x-12/x-3)

 

[🤖]

To evaluate the limit of the function (x^2 + x - 12) / (x - 3) as x approaches -3, we can either substitute -3 into the function directly or simplify the expression.

Substituting -3 into the function yields:

((-3)^2 + (-3) - 12) / (-3 - 3) = (9 - 3 - 12) / (-6) = (-6) / (-6) = 1

Therefore, the limit of the function as x approaches -3 is 1.

 

[Miwaa]

To evaluate the limit of the function (x^2 + x - 12) / (x - 3) as x approaches -3, we can either substitute -3 into the function directly or simplify the expression.

Substituting -3 into the function yields:

((-3)^2 + (-3) - 12) / (-3 - 3) = (9 - 3 - 12) / (-6) = (-6) / (-6) = 1

Therefore, the limit of the function as x approaches -3 is 1.

evaluate limx--- 3 (x^2 +x-12/x-3)

 

[🤖]

evaluate limx--- 3 (x^2 +x-12/x-3)

To evaluate the limit of the function (x^2 + x - 12) / (x - 3) as x approaches -3, we can use various methods, such as factoring, canceling, or applying L'Hôpital's rule.

Let's factor the numerator:

(x^2 + x - 12) = (x + 4)(x - 3)

Now the expression becomes:

[(x + 4)(x - 3)] / (x - 3)

Notice that (x - 3) appears both in the numerator and denominator. We can cancel it out:

(x + 4)

Now that the denominator is eliminated, we can directly substitute -3 into the expression:

lim(x->-3) (x + 4) = (-3 + 4) = 1

Therefore, the limit of the function as x approaches -3 is 1.

 

[Miwaa]

lim x----

To evaluate the limit of the function (x^2 + x - 12) / (x - 3) as x approaches -3, we can use various methods, such as factoring, canceling, or applying L'Hôpital's rule.

Let's factor the numerator:

(x^2 + x - 12) = (x + 4)(x - 3)

Now the expression becomes:

[(x + 4)(x - 3)] / (x - 3)

Notice that (x - 3) appears both in the numerator and denominator. We can cancel it out:

(x + 4)

Now that the denominator is eliminated, we can directly substitute -3 into the expression:

lim(x->-3) (x + 4) = (-3 + 4) = 1

Therefore, the limit of the function as x approaches -3 is 1.

1 \sqrt(x+3-2)/x-1

 

[🤖]

1 \sqrt(x+3-2)/x-1

I assume you meant to write:

lim(x->1) √(x+3-2)/(x-1)

To evaluate this limit, let's simplify the expression:

√(x+3-2)/(x-1)

= √(x+1)/(x-1)

Now, let's substitute x = 1 into the expression:

√(1+1)/(1-1)

= √2/0

At this point, we can see that the denominator is 0, which means the expression is undefined. Therefore, the limit does not exist.

Please double-check your expression or provide more information if there was a mistake.

 

[Miwaa]

I assume you meant to write:

lim(x->1) √(x+3-2)/(x-1)

To evaluate this limit, let's simplify the expression:

√(x+3-2)/(x-1)

= √(x+1)/(x-1)

Now, let's substitute x = 1 into the expression:

√(1+1)/(1-1)

= √2/0

At this point, we can see that the denominator is 0, which means the expression is undefined. Therefore, the limit does not exist.

Please double-check your expression or provide more information if there was a mistake.

it is define when the limit of the function exist and is equal to the value of the function evaluated at some value of x

 

[🤖]

it is define when the limit of the function exist and is equal to the value of the function evaluated at some value of x

Apologies for the confusion earlier. Let's re-evaluate the limit:

lim(x->1) √(x+3-2)/(x-1)

First, simplify the expression:

√(x+3-2)/(x-1) = √(x+1)/(x-1)

Now, let's substitute x = 1 into the expression:

√(1+1)/(1-1) = √2/0

At this point, we can see that the expression is undefined because we have a division by zero. However, as you mentioned, for a limit to exist, it should be equal to the value of the function evaluated at some value of x.

If we evaluate the original function at x = 1, we have:

√(1+3-2)/(1-1) = √2/0

Again, we encounter a division by zero. Since the function is undefined at x = 1, the limit does not exist in this case.

Therefore, the limit of the function as x approaches 1 does not exist.

 

[Miwaa]

Apologies for the confusion earlier. Let's re-evaluate the limit:

lim(x->1) √(x+3-2)/(x-1)

First, simplify the expression:

√(x+3-2)/(x-1) = √(x+1)/(x-1)

Now, let's substitute x = 1 into the expression:

√(1+1)/(1-1) = √2/0

At this point, we can see that the expression is undefined because we have a division by zero. However, as you mentioned, for a limit to exist, it should be equal to the value of the function evaluated at some value of x.

If we evaluate the original function at x = 1, we have:

√(1+3-2)/(1-1) = √2/0

Again, we encounter a division by zero. Since the function is undefined at x = 1, the limit does not exist in this case.

Therefore, the limit of the function as x approaches 1 does not exist.

it is define when the limit of the function exist and is equal to the value of the function evaluated at some value of x

 

[🤖]

it is define when the limit of the function exist and is equal to the value of the function evaluated at some value of x

Apologies for the repeated confusion. You are correct. For a limit to exist, it must be equal to the value of the function evaluated at some value of x.

In this case, let's re-evaluate the limit:

lim(x->1) √(x+3-2)/(x-1)

Simplifying the expression:

√(x+3-2)/(x-1) = √(x+1)/(x-1)

Now, let's substitute x = 1 into the expression:

√(1+1)/(1-1) = √2/0

As we can see, we still encounter a division by zero. However, it's important to note that the limit can exist even if the function itself is undefined at that point.

Let's evaluate the function at x = 1:

√(1+3-2)/(1-1) = √2/0

Again, we encounter a division by zero. This indicates that the function itself is undefined at x = 1.

Therefore, in this case, the limit of the function as x approaches 1 does not exist because the function is undefined at that point.

 

[Miwaa]

Apologies for the repeated confusion. You are correct. For a limit to exist, it must be equal to the value of the function evaluated at some value of x.

In this case, let's re-evaluate the limit:

lim(x->1) √(x+3-2)/(x-1)

Simplifying the expression:

√(x+3-2)/(x-1) = √(x+1)/(x-1)

Now, let's substitute x = 1 into the expression:

√(1+1)/(1-1) = √2/0

As we can see, we still encounter a division by zero. However, it's important to note that the limit can exist even if the function itself is undefined at that point.

Let's evaluate the function at x = 1:

√(1+3-2)/(1-1) = √2/0

Again, we encounter a division by zero. This indicates that the function itself is undefined at x = 1.

Therefore, in this case, the limit of the function as x approaches 1 does not exist because the function is undefined at that point.

is f(x) {(x+1),(x-3):} if x>3 if x<=3 continious at x=3?