Continuity of Functions

Name: Continuity of Functions
Author: StemPy Lab

A graph with no break is continuous, and a graph with a gap is not. Turn that picture into a test with left-hand and right-hand limits, name the three kinds of break, and check piecewise functions. Then use the Intermediate Value Theorem to show that an equation has a root. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topic of A-Level, IB and AP.

3 lessons, about 1 h 15 min3 simulations10 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Continuity at a point
A function is continuous at a point when its graph passes through the point without a break. In symbols, the left-hand limit, the right-hand limit and the value of the function are all equal. When one of the three fails, the graph has a break. The break is removable, a jump or infinite.
1 simulation1 practice question1 Python program3 problems1 Python lab
Read the lesson
Lesson 2about 25 min
Continuity on an interval and of piecewise functions
A function is continuous on an interval when it is continuous at every point of it. On a closed interval the end points need one-sided continuity. Sums, differences, products, quotients and compositions of continuous functions are continuous, and polynomials, sine, cosine and exponentials are continuous everywhere. For a piecewise function, check each joining point.
1 simulation1 practice question1 Python program4 problems
Read the lesson
Lesson 3about 25 min
The Intermediate Value Theorem
If $f$ is continuous on a closed interval $[a, b]$ , it takes every value between $f(a)$ and $f(b)$ . This is the Intermediate Value Theorem. A change of sign of a continuous function therefore traps a root, and halving the interval again and again, the bisection method, finds that root as closely as you like.
1 simulation1 practice question1 Python program3 problems1 Python lab1 question set1 note
Read the lesson

Test Your Learning

Continuity of Functions: Practice Paper

15 questions · 20 min

Not started

Your teacher

StemPy Lab

← All Courses

← PreviousDifferentiability and the Rules of Differentiation →

More onFunctions and Calculus › Continuity and Differentiability

Discussion (0)

Loading…

Continuity of Functions

Course outline (3 lessons)

Continuity at a point

Continuity on an interval and of piecewise functions

The Intermediate Value Theorem

Test Your Learning

Your teacher

1 follower

Discussion (0)

Want to go further?