What does continuous at a point mean?
hercegvm
Open question
2022-08-22
Answer & Explanation
zoranovxp
Beginner2022-08-23Added 7 answers
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.
New Questions in Differential Calculus
What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?
How do I find the y-intercept of a parabola?
What are the vertices of ?
How to determine the rate of change of a function?
Why are the tangents for 90 and 270 degrees undefined?
How to find the center and radius of the circle ?
What is multiplicative inverse of a number?
How to find the continuity of a function on a closed interval?
How do I find the tangent line of a function?
How to find vertical asymptotes using limits?
How to find the center and radius of the circle ?
Let f be a function so that (below). Which must be true?
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
(A) I (B) II (C) I and II (D) I and III (E) II and IIIHow to find the center and radius of the circle given ?
How to find the center and radius of the circle ?
How to identify the center and radius of the circle ?
