If α is a repeated root of a x 2 + b x + c = 0 then lim x → α sin ( a x 2 + b x + c ) ( x − α ) 2 is Options: A . &nbsp 0 B . &nbsp a C . &nbsp b D . &nbsp c

Answer: Option B : B lim x → α sin ( a x 2 + b x + c ) ( x − α ) 2 = lim x → α sin a ( x − α ) ( x − α ) ( x − α ) 2 = lim x → α sin a ( x − α ) 2 a ( x − α ) 2 × a = a

If α is a repeated root of ax2+bx+c=0 then limx→αsin(ax2+bx

Discussion Forum : Limits Continuity And Differentiability

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

Options:

A .

0

B .

a

C .

b

D .

c

Answer: Option B
:
B

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

= lim x \to α \frac{sin a (x - α)^{2}}{a (x - α)^{2}} \times a = a

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Discussion Forum : Limits Continuity And Differentiability

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