
Relations and Functions

Inverse Trigonometric Functions

Matrices

Determinants

Continuity and Differentiability

Application of Derivatives

Integrals

Differential Equations

Probability

Vectors

Three  Dimensional Geometry

Application of Integrals

Applications of Calculus in Commerce and Economics

Linear Regression

Linear Programming
Indeterminate Forms
If the limits of f(x) and g(x) are equal to 0, as x tends to a, then f(x)/ g(x) is said to assume indeterminate form 0/0.
Some other indeterminate forms are ∞/∞, ∞  ∞, 0×∞, 00, 1∞ and ∞0.
L’ Höpital’s rule
If f(x) and g(x) are differentiable, g'(x) is not equal to zero for all x in the interval (a – h, a + h), except possibly at x = a, limits of f(x) and g(x) are equal to zero when x tends to a and limit of f'(x) / g' (x) exists finitely or infinitely when x tends to a, then the limit of f(x)/ g(x) when x tends to a is equal to the limit of f'(x) / g' (x) when x tends to a.
L’ Höpital’s rule remains valid when the limit of f(x) as x tends to a is replaced by one sided limits.
L’ Höpital’s rule remains valid when the limits tend to negative infinity.
Keywords: L’ Höpital’s rule, Indeterminate forms
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