Outline of Contents
Target Audience: High School Students, College Freshmen and Sophomores, students preparing for the International Baccalaureate (IB), AP Calculus AB, AP Calculus BC, A Level, Singapore/GCE A-Level; Class 11/12 students in India preparing for ISC/CBSE and Entrance Examinations like the IIT-JEE/AIEEE Anyone else who needs this Tutorial as a reference!
More advanced cases of evaluating limits, conditions for continuity of functions, common approximations used while evaluating limits for ln ( 1 + x ), sin (x); continuity related problems for more advanced functions than the ones in the first group of problems (in the last tutorial).
Finding the values of 'x' for which a given function is continuous. Limits involving change of variables. Determining whether given functions are continuous at specified points. Limits involving approximations and series expansions.
Limits involving polynomials of 'x' in the numerator and denominator; limits involving series expansions, trigonometric, exponential and logarithmic functions. Coverage 0/0 and Infinity/Infinity kinds of limits.
... apart from this, we will also find the limits for a lot more interesting functions and we will also learn to apply L'Hospital's rule.
MCQ Quiz on Single Variable Calculus mainly focused on Functions, Limits, Continuity- Set 2
Companion MCQ Quiz for Functions, Limits, Continuity #2 - test how much you know about the topic. Your score will be e-mailed to you at the address you provide.
Other Calculus Tutorials
Quick and introductory definitions related to Funtions, Limits and Continuity
Functions, Limits and Continuity - Solved Problem Set I - The Domain, Range, Plots and Graphs of Functions; L'Hospital's Rule-
Functions, Limits and Continuity - Solved Problem Set II - Conditions for Continuity, More Limits, Approximations for ln (1+x) and sin x for infinitesimal values of x
Functions, Limits and Continuity - Solved Problem Set III - Continuity and Intermediate Value Theorems
Introductory concepts and definitions related to Differentiation - Basic formulas, Successive Differentiation, Leibnitz, Rolle and Lagrange Theorems, Maxima , Minima, Convexity, Concavity, etc
Differential Calculus - Solved Problem Set I - Common Exponential, Log , trigonometric and polynomial functions
Differential Calculus - Solved Problem Set II - Derivability and continuity of functins - Change of Indepndent Variables - Finding N-th Derivatives -
Differential Calculus - Solved Problems Set III- Maximia, Minima, Extreme Values, Rolle's Theorem
Differential Calculus - Solved Problems Set IV - Points of Inflexion, Radius of Curvature, Curve Sketching
Differential Calculus - Solved Problems Set V - Curve Sketching, Parametric Curves
Introducing Integral Calculus - Definite and Indefinite Integrals - using Substitution , Integration By Parts, ILATE rule
Integral Calculus - Solved Problems Set I - Basic examples of polynomials and trigonometric functions, area under curves
Integral Calculus - Solved Problems Set II - More integrals, functions involving trigonometric and inverse trigonometric ratios
Integral Calculus - Solved Problems Set III - Reduction Formulas, Using Partial FractionsI
Integral Calculus - Solved Problems Set IV - More of integration using partial fractions, more complex substitutions and transformations
Integral Calculus - Solved Problems Set V- Integration as a summation of a series
Introduction to Differential Equations and Solved Problems - Set I - Order and Degree, Linear and Non-Linear Differential Equations, Homogeneous Equations, Integrating Factor
Differential Equations - Solved Problems - Set II - D operator, auxillary equation, General Solution
Differential Equations - Solved Problems - Set III - More Differential Equations
Differential Equations - Solved Problems - Set IV