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Chapter: 11th Mathematics : UNIT 9 : Differential Calculus Limits and Continuity

Some important other limits

Differential Calculus: Limits : Some important limits

Some important other limits


Result 9.2


Result 9.3


Proof

We know that a x ,loga x are inverses of each other.

Since log f (x) is the inverse of  exp( f (x)), exp(log f (x)) = f (x).

Therefore, ax  = exp(loga x)


Result 9.4



Some important limits without proof


This number e is also known as transcendental number in the sense that e never satisfies a polynomial (algebraic) equation of the form





EXERCISE 9.4

Evaluate the following limits‚ÄČ:





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