Q. 0 - Calculus

Question

Problem Zero: Read the section and make your own summary of the material. 

Step-by-Step Solution

Answer

Summary has been explained.

Step 1. Given information

We have to read the section and make your own summary of the material. 

Step 2. Summary

A function f is continuous on an interval I if it is continuous at every point in the interior of I, right continuous at any closed left endpoint, and left continuous at any closed right endpoint.

Suppose f is discontinuous at x = c. We say that x = c is a

Removable discontinuity if $\underset{x\to c}{lim} f\left(x\right)$ exists but is not equal to f (c);

Jump discontinuity if $\underset{x\to c^{†}}{lim} f\left(x\right)$ and $\underset{x\to c^{-}}{lim} f\left(x\right)$ both exist but are not equal;

Infinite discontinuity if one or both $\underset{x\to c^{-}}{lim} f\left(x\right)$ and $\underset{x\to c^{-}}{lim} f\left(x\right)$ is infinite.

If f(x) is continuous on a closed interval la, bl, then for any 'K' strictly between f(a) and f(b), there exists at least one c = (a, b) such that f(c) = K.

If f(x) is continuous on a closed interval [a, b], then there exist values 'M'and "m' in the intervalla, [a,b] such that f(M) is the maximum value of f(x) on [a, b] and f(m) is the minimum value of f(x) on [a, b]. 7. A function f(x) can change sign (from positive to negative or vice versa) at a point.x = c only if f(x) is

zero, undefined, or discontinuous at r = c.