If `x_(1)` and `x_(2)` are the real and distinct roots of `ax^(2)+bx+c=0` then prove that `lim_(xtox1) (1+sin(ax^(2)+bx+c))^((1)/(x-x_(1)))=e^(a(x_(1)

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If `x_(1)` and `x_(2)` are the real and distinct roots of `ax^(2)+bx+c=0` then prove that `lim_(xtox1) (1+sin(ax^(2)+bx+c))^((1)/(x-x_(1)))=e^(a(x_(1)

If `x_(1)` and `x_(2)` are the real and distinct roots of `ax^(2)+bx+c=0` then prove that `lim_(xtox1) (1+sin(ax^(2)+bx+c))^((1)/(x-x_(1)))=e^(a(x_(1)-x_(2))).`
A. does not exist
B. 1
C. `oo`
D. `(1)/(2)`

Monjur Alahi

7 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

`ax^(2)+bx+c=a(x-x_(1))(x-x_(2))`
`underset(xtox1)lim(1+sin(ax^(2)+bx+c))^((1)/(x-x_(1)))" "(1^(oo))" form")`
`=e^(underset(xtox_(1))lim(sin(a(x-x_(1))(x-x_(2))))/((x-x_(1))))`
`=e^(underset(xtox_(1))lim(sin(a(x-x_(1)).(x-x_(2))))/(a(x-x_(1))(x-x_(2))).a(x-x_(2)))`
`=e^(a(x_(1)-x_(2)))`

7 views Answered 2023-02-05 15:29