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Problem on limits

17/01/2017 0 0

Find:   limit x→16 ( x¼ - 2 ) /  (x - 16)

We can rewrite the problem as 

limit x→16 ( x¼ - 16¼ )/(x - 16).  

[ use standard formula of.    limit x→a {(x^n - a^n)/(x - n)} = n a ^n-1}

Here n = 1/4 and a = 16 ∴ by substituting these values in the standard formula

limit x→16 ( x¼ - 2 )/(x - 16) = 1/4 • 16 ^ (1/4 - 1)

                                                   = 1/4 • 16 ^ (- 3/4)

                                                    = 1/4 • ( 1/8 )

                                                    = 1/8


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