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If f(x)= -(25-x2)½, find the value of lim x tends to 1, f(x)- f(1)/x-1. please lemme know the answer ...am in a fixpleasee

AMRUTHA , 9 Years ago
Grade
anser 1 Answers
BALAJI ANDALAMALA

Last Activity: 8 Years ago

\lim_{x->1}\frac{f(x)-f(1)}{x-1} is of the form 0/0 .

Using L’Hospital rule ,differentiate numerator and denominator with respect to x.

We get\lim_{x->1}\frac{f(x)-f(1)}{x-1} =\lim_{x-->1}f'(x)

f'(x)=-\frac{1}{2}(25-x^2)^{\frac{-1}{2}}(-2x)
\lim_{x-->1}f'(x)=f'(1)=-\frac{1}{2}(25-1^2)^{\frac{-1}{2}}(-2) = \frac{1}{2\sqrt{6}}

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