CBSE Class 11-commerce Maths Limits and Derivatives
Introduction and Algebra of Limits
Limit of polynomial function can be computed using substitution or algebra of limits.Limits of Rational Functions
For computing the limit of a Rational Function use Method of Direct Substitution, if the result is an Indeterminate form.Limits of Trigonometric Functions
Use sandwich/Squeeze Theorem to find the limit as x approaches zero of sin x over x.Evaluate the limits of trigonometric functions.Logarithmic and Exponential Limits
Logarithmic and Exponential LimitInfinite Limits
Infinite LimitMeaning of Derivatives
The derivative is the instantaneous rate of change in terms of physics.
The derivative is the slope of the tangent at a point.Sum and Difference Rule
If f(x) is a differentiable function and c is a constant then by constant multiple rule (cf(x) )'= c (f '(x))
If f and g are differentiable functions, then by sum and difference rule we have[f(x) ± g(x)]' = [f '(x) ± g'(x)]
The derivative of a function f(x) at a point x = a is f '(a).Product and Quotient Rule
If there are two differential functions f(x) and g(x) then (f(x) g(x)) =f'(x)g(x)+f(x)g'(x) using product rule.
