If x1andx2 are the real and distinct roots of ax2+bx+c=0, then prove that n→x1lim{1+sin(ax2+bx+c)}x−x11=ea(x1−x2)

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If {x}_{{1}}{{and}}{x}_{{2}} are the real and distinct roots o

Question

If $x_{1} and x_{2}$ are the real and distinct roots of $a x^{2} + b x + c = 0,$ then prove that $n \to x_{1} lim {1 + sin (a x^{2} + b x + c)}^{\frac{1}{x - x _{1}}} = e^{a (x_{1} - x_{2})}$

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x_{1} and x_{2}

are the real and distinct roots of

a x^{2} + b x + c = 0,

then prove that

n \to x_{1} lim {1 + sin (a x^{2} + b x + c)}^{\frac{1}{x - x _{1}}} = e^{a (x_{1} - x_{2})}

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Question Text

x_{1} and x_{2}

are the real and distinct roots of

a x^{2} + b x + c = 0,

then prove that

n \to x_{1} lim {1 + sin (a x^{2} + b x + c)}^{\frac{1}{x - x _{1}}} = e^{a (x_{1} - x_{2})}