Category: Differential Calculus / IIT JEE MAINS/ADVANCED-FREE STUDY METERIAL
It contains functions , limits,continuity,differentibility, application of derivatives concepts and solved examples (objective + subjective ) for JEE mains/advanced level
1 Function :- Number System, Intervals, Quadratic Graphs and Solving rational Inequalities, Trigonometric Graphs and Solving Trigonometric equations and Inequalities, Exponential and Logarithmic functions solving equation and Inequalities, The Absolute Value of A Real Number, Mode Functions, Graphs, Solving Equation and Inequalities, Integer Function, Fractional part function, Graphs solving equation and Inequities, Signum function graph solving equation and Inequalities, Max-min Functions, Inverse Functions (Bijective Function), Periodic Function, Definition of Function(one-one, many-one, on-to, into), Algebra of Functions, Composite Function,Even and Odd Function, Elementary Transformation of Graphs, Cubic Function, Linear/Linear, Linear/Quadratic, Quadratic/Quadratic, Some Special Functions etc.
2 Limits :- Indeterminate Forms, Some Standard Results and there explanations, Algebra of Limits,Composite Function ,Sandwich and other Standard Theorems, Expansions,Left Hand Limits and Right Hand Limits, Solving Technics to evaluate geometrical problems, Algebraic Problems, Trigonometric Problems,
Co-efficient Problems, Fractional and GIF Related Problems, Etc. Related to Limits.
3 Continuity :- Meaning of Continuity, Algebra of Continuous function, Continuity of Composite function, Continuity of f(x) at x = c,Continuity of f(x) in Open Interval (a, b), Continuity of f(x) in Closed Interval [a, b],Discontinuity of f(x) at x = c,Removable Discontinuity, Oscillating Discontinuity, Uniqueness of Standard Results on Continuous Functions,Intermediate Value Theorem (IVT),L’ Hospital Rule (Derivative Rule) Etc.
4 Differentiability and Derivatives :- Derivative of a Function,One-Sided Limits,Theorems on Derivatives of Functions, Some Useful Results, Differentiability of a Function, Theorem 1,Differentiability of y = f(x) in (a, b),Theorem 2, Differentibility of y=f(x) in Closed Interval (a, b), Method for Discussing Differentiability and Continuity of y = f(x) and Application Etc.
5 Application of Derivatives : –
Tangent and Normal, Angle Between Two Curves, Rolle’s Theorem,Lagrange’s Mean Value Theorem (MVT),
Monotonocity,Tests for Monotonocity,
Local Maxima and Local Minima,Critical Points, Methods For Testing Critical Points,
First Derivative Test, Second Derivative Test,
nth Derivative Test,Extremum Points, Absolute Max./Min. Points,Point of Inflection of f(x) and there Applications Etc……