The function fx - sina-1x - sinx-x for x 0 - is continuous at x - 0- the a-b-c should satisfy

The correct options are A c = 1/2 C a = 3/2 D b ≠ 0 x → 0^ limsin(a + 1)x + sin x/x = a + 2 and nbsp; x → 0^+lim nbsp;x + bx^2 x/bx^3/2(√(x ...

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Continuity of a Function

the function ...

Question

the function f(x) = $⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{s i n (a + 1) x + s i n x}{x} f o r x < 0 c f o r x = 0 \frac{(x + b x^{2})^{1 / 2} - x^{1 / 2}}{b x^{3 / 2}} f o r x > 0 \end{matrix}$ , is continuous at x = 0, the a,b,c should satisfy

a = -3/2

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\neq

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c = 1/2

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b = 0,

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a, b, c

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{sin (a + 1) x + sin x}{x} & f o r x < 0 = c & f o r x = 0 = \frac{{(x + b x^{2})}^{1 / 2} - x^{1 / 2}}{b x^{3 / 2}} & f o r x > 0 \end{matrix}

x = 0

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{(x + b x^{2})^{1 /_{2}} - x^{1 / 2}}{b x^{3 / 2}} & x > 0 c & x = 0 \frac{sin (a + 1) x + sin x}{x} & x < 0 \end{matrix}

x = 0

a, b, c

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} f (x) = \frac{sin (a + 1) x + sin x}{x} & for x < 0 = c & for x = 0 \frac{(x + b x^{2})^{\frac{1}{2}} - x^{\frac{1}{2}}}{b x^{\frac{1}{2}}} & for x > 0 \end{matrix}

x = 0

a, b, c

f (x) = \frac{sin (a + 1) x + sin x}{x}, f o r x < 0

c, f o r x = 0

= \frac{{(x + b x)}^{1 / 2} - x^{1 / 2}}{{b x}^{1 / 2}}, f o r x > 0

x = 0

a, b

c

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{sin (a + 1) x + sin x}{x} & , x < 0 c & , x = 0 \frac{\sqrt{x + b x^{2}} - \sqrt{x}}{x^{3 / 2}} & , x > 0 \end{matrix}

x = 0

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