Does 1 x have a limit?

Does 1 x have a limit?

1 Answer. Remark: If you are to determine whether the limit exists, then the answer is no since it is an infinite limit.

How do you find the limit as x approaches 1?

The value as x approaches 1 from both the left and the right approaches 1.5. Since the limit from both the left and the right are the same, then the overall limit as x approaches 1 is 1.5. lim x → 1 f ( x ) = 1.5 .

What is the limit of 1 x as x approaches infinity?

zero

Does the limit of 1 x 2 exist?

Actually, if you take 1/|x-2|, the limit is infinity, therefore the limit does NOT exist.

What is the limit as x approaches 0?

The limit of f(x) as x approaches zero is undefined, since both sides approach different values. Visually, , , and is undefined.

Can a limit exist at infinity?

As a general rule, when you are taking a limit and the denominator equals zero, the limit will go to infinity or negative infinity (depending on the sign of the function). So when would you put that a limit does not exist? When the one sided limits do not equal each other.

What makes a limit not exist?

Limits typically fail to exist for one of four reasons: The function doesn’t approach a finite value (see Basic Definition of Limit). The function doesn’t approach a particular value (oscillation). The x – value is approaching the endpoint of a closed interval.

Can a graph be continuous at a corner?

A continuous function doesn’t need to be differentiable. There are plenty of continuous functions that aren’t differentiable. Any function with a “corner” or a “point” is not differentiable.

What is the slope of a corner?

A corner is one type of shape to a graph that has a different slope on either side. It is similar to a cusp. Here, the derivative at x=0 is undefined, because the slope on the left side is 1 , but the slope on the right side is −1 .

Why is 0 0 indeterminate?

When calculus books state that 00 is an indeterminate form, they mean that there are functions f(x) and g(x) such that f(x) approaches 0 and g(x) approaches 0 as x approaches 0, and that one must evaluate the limit of [f(x)]g(x) as x approaches 0. In fact, 00 = 1! …

Is 0 * 0 an indeterminate form?

According to some Calculus textbooks, 0^0 is an “indeterminate form”. When evaluating a limit of the form 0^0, then you need to know that limits of that form are called “indeterminate forms”, and that you need to use a special technique such as L’Hopital’s rule to evaluate them.