# What does continuous at a point mean?

The simplest explanation is that you must draw a curve through the point without lifting your pen. Lifting your pen would be a discontinuity.

Continuity at a point allows us to define and come up with theorems about continuous functions. The continuous functions (in their domain) are: polynomials, rationals, roots, trigonometric, exponential, and logarithmic. Be careful because these functions are not continuous for all reals; it is important to note that there is a restriction "in their domain".

For calculus, you will notice most theorems require continuity, such as the IVT, MVT, derivative tests, and FTC to name a few.

By signing up, you agree to our Terms of Service and Privacy Policy

Continuous at a point means that a function is defined at that point and the limit of the function as the input approaches that point exists and is equal to the value of the function at that point.

By signing up, you agree to our Terms of Service and Privacy Policy

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 find #lim root3(t+4)-root3t# as #t->oo#?
- What is the limit as x approaches 0 of #cotx/lnx#?
- What is the limit of #(x^3-10)/x^2# as x goes to infinity?
- How do you use the epsilon delta definition to find the limit of #(x^2 + 4x) # as x approaches #2#?
- What is an example of a function g(x) that is continuous for all values of x except x=-1, where it has a non removable discontinuity?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7