(lim)(x->1)(a x^2+b x+c)/(c x^2+b x+a),"...

`(lim)_(x->1)(a x^2+b x+c)/(c x^2+b x+a),""a+b+c!=0`

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Knowledge Check

Find the value of the expression: ((x^(a+b))^(2) xx (x^(b+c))^(2) xx (c^(c+a))^(2))/(x^(a) x^(b) x^( c))^(4) , If x=2, a=1, b =2, c=3

A

16

B

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C

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D

1

Let a =lim _(xto0) (ln (cos 2x ))/( 3x ^(2)) , b = lim _(xto0) (sin ^(2) 2x )/(x (1-e ^(x))), c = lim _(x to 1) (sqrtx-x )/( ln x). Then a,b,c satisfy :

A

`a lt b lt c`

B

`b lt c lt a`

C

`a lt c lt b`

D

`b lt a lt c`

lim_(x to 0)((a^(x) + b^(x) + c^(x))/3)^(2//x), a,b,c gt 0 is equal to:

A

abc

B

`a^(2)b^(2)c^(2)`

C

`(abc)^(2//3)`

D

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