Method of substitution:

To calculate  by the process of substitution we need different substitutions. For example if we replace x by a + h, then the provided limit becomes  (as x→a h→0).  Similarly as we may use different substitution like substitute x by 2h, 1/h etc. For example,  (putting x = a + h)

Example: Calculate 

Key concept:     First of all replacement cos^-1x = θ, use the process of substitution.

Solution:             Let cos^-1x = θ, then x = cosθ

      Now  as x -> 1 θ -> cos^-1(1), i.e. θ -> 0

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