f(x)={3x2sin2x2 ; if x<0x2+2x+c1−3x2; if x≥0, x≠13 0 ; if x=13, then in order that 'f' be a continuous at x=0, the value of 'c' is

LHL=RHL limx→03x2sin2x2=limx→0x2+2x+c1−3x2 ⇒3×2=c ∴c=6

f(x)={3x2sin2x2 ; if x<0x2+2x+c1−3x2; if x≥0, x≠13 0 ; if x=13, then in order that 'f' be a continuous at x=0, the value of 'c' is

LHL=RHL limx→03x2sin2x2=limx→0x2+2x+c1−3x2 ⇒3×2=c ∴c=6

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$f (x) = {\begin{matrix} \frac{3}{x^{2}} sin 2 x^{2}; if x < 0 \\ \frac{x^{2} + 2 x + c}{1 - 3 x^{2}}; if x \geq 0, x \neq \frac{1}{\sqrt{3}} \\ 0; if x = \frac{1}{\sqrt{3}} \end{matrix},$ then in order that $' f'$ be a continuous at $x = 0,$ the value of $' c'$ is

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$L H L = R H L$

$\lim_{x \to 0} \frac{3}{x^{2}} \sin 2 x^{2} = \lim_{x \to 0} \frac{x^{2} + 2 x + c}{1 - 3 x^{2}}$

$\Rightarrow 3 \times 2 = c$

$∴ c = 6$

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f(x)={3x2sin2x2 ; if x<0x2+2x+c1−3x2; if x≥0, x≠13 0 ; if x=13, then in order that 'f' be a continuous at x=0, the value of 'c' is

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$f (x) = {\begin{matrix} \frac{3}{x^{2}} sin 2 x^{2}; if x < 0 \\ \frac{x^{2} + 2 x + c}{1 - 3 x^{2}}; if x \geq 0, x \neq \frac{1}{\sqrt{3}} \\ 0; if x = \frac{1}{\sqrt{3}} \end{matrix},$ then in order that $' f'$ be a continuous at $x = 0,$ the value of $' c'$ is