Some important other 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 :