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in Continuity and Differentiability by (26.9k points)
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Determine whether \(f(x) = \begin{cases} \frac{sinx^2}{x}, & x ≠{0}\\ 0, &x={ 0} \end{cases} \) is continuous at x = 0 or not.

1 Answer

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Best answer

Formula :

(i) \(\lim\limits_{x \to 0}\frac{sinx}{x}=1\)

(ii) A function f(x) is said to be continuous at a point x=a of its domain, if
\(\lim\limits_{x \to a}f(x)\) = f(a)

Hence,

f(x) is continuous at x=0

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