f(x)=3x2sin⁡2x2 if x<0x2+2x+c1−3x2 if x≥0,x≠13 then in order that f be continuous at x=0 then 0 if x=13the value of c is

Ltx=0− fx=Ltx=0− 3x2sin2x2=6 Ltx→0 sin2x22x2=6Ltx=0+ fx=Ltx=0+ x2+2x+c1−3x2=c1=c∴f is continuous ∴c=6

f(x)=3x2sin⁡2x2 if x<0x2+2x+c1−3x2 if x≥0,x≠13 then in order that f be continuous at x=0 then 0 if x=13the value of c is

Ltx=0− fx=Ltx=0− 3x2sin2x2=6 Ltx→0 sin2x22x2=6Ltx=0+ fx=Ltx=0+ x2+2x+c1−3x2=c1=c∴f is continuous ∴c=6

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

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$\underset{x = 0^{-}}{L t} f (x) = \underset{x = 0^{-}}{L t} \frac{3}{x^{2}} \sin 2 x^{2} = 6 \underset{x \to 0}{L t} \frac{\sin 2 x^{2}}{2 x^{2}} = 6$

$\underset{x = 0^{+}}{L t} f (x) = \underset{x = 0^{+}}{L t} \frac{x^{2} + 2 x + c}{1 - 3 x^{2}} = \frac{c}{1} = c$

$∴ f is continuous ∴ c = 6$

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f(x)=3x2sin⁡2x2 if x<0x2+2x+c1−3x2 if x≥0,x≠13 then in order that f be continuous at x=0 then 0 if x=13the value of c is

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