If - is a repeated root of a x2-b x-c-0 then lim x -sinx2-b x-c-x-2 isA- cB- 0C- aD- b

The correct option is C x→αlimsin(ax^2+bx+c)/(x α)^2 = x→αlimsin a(x α)(x α)/(x α)^2 = x→αlimsin a(x α)^2/a(x α)^2× a = a ...

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Standard Limits to Remove Indeterminate Form

If α is a rep...

Question

If $α$ is a repeated root of $a x^{2} + b x + c = 0$ then $lim x \to α \frac{sin (a x^{2} + b x + c)}{(x - α)^{2}}$ is

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\lim_{x \to α} \frac{\tan (a x^{2} + b x + c)}{{(x - α)}^{2}}

α

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

lim x \to α \frac{tan (a x^{2} + b x + c)}{(x - α)^{2}} =

α

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

lim x \to α \frac{sin (a x^{2} + b x + c)}{(x - α)^{2}}

If $α$ is a reapeated root of $a x^{2} + b x + c = 0,$ then ${lim}_{x \to a} \frac{t a n (a x^{2} + b x + c)}{(x - α)^{2}}$ is

α

β

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

l i m x \to a \frac{1 - c o s (a x^{2} + b x + c)}{(x - α)^{2}}

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