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If underset(xrarroo)(lim)xlog(e)(|(alpha...

If `underset(xrarroo)(lim)xlog_(e)(|(alpha//x,1,gamma),(0,1//x,beta),(1,0,1//x)|)=-5.` where `alpha, beta, gamma` are finite real numbers, then

A

a = 2

B

b = -4

C

c = 2

D

a + b + c = 8

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`underset(xrarr0)(lim)(ae^(x)+bcosx+ce^(-x))/(e^(2x)-2e^(x)+1)`
`rArr underset(xrarr0)(lim)(a(1+x+(x^(2))/(2)+...)+b(1-(x^(2))/(2)...)+c(1-x+(x^(2))/(2)))/(x^(2)).((x)/(e^(x)-1))^(2)=4`
`rArr" "a+b+c=0, a-c=0 rArr a=c`
`rArr" "(a-b+c)/(c)=4`
`rArr" "a-b+c=8 rArr 2b = -8 rArr b=-4`
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