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The Chemical Science
Limits and Derivatives
Calculus is that branch of mathematics which mainly deals with the study of change in the value of a function as the points in the domain changes.
I. Limit
Limit of a function f(x) at x = a is the behaviors of f(x) at x = a.
x → a–: Means that ‘x’ takes values less than ‘a’ but not ‘a’.
x → a+: Means that ‘x’ takes values greater than ‘a’ but not ‘a’.
x → a: Read as ‘x’ tends to ‘a’, means that ‘x’ takes values very close to ‘a’ but not ‘a’.
II. Evaluation Methods
Direct substitution method
Factorisation method
Rationalisation method
Using standard results.
III. Algebra of Limits:
For functions f and g the following holds;
IV. Standard Results
V. Derivatives
VI. Algebra of Derivatives
For functions f and g are differentiable following holds-
VII. Standard Result
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