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If f(x)= -(25-x 2 ) ½ , find the value of lim x tends to 1, f(x)- f(1)/x-1. please lemme know the answer ...am in a fix pleasee

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 fix  pleasee
 

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1 Answers

BALAJI ANDALAMALA
askIITians Faculty 78 Points
6 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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