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Integral Calculus

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

AMRUTHA

10 Years agoGrade

1 Answer

BALAJI ANDALAMALA

10 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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