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Let f(x)={|x-2|+a^2-6a+9, x < 2 and 5-2x...

Let `f(x)={|x-2|+a^2-6a+9, x < 2 and 5-2x, x >= 2` If `lim_(x->2) [f(x)]` existsn the possible values a can take is/are (where [.] represents the grestest integer function)

A

2

B

`5/2`

C

3

D

`7/2`

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The correct Answer is:
B
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VIKAS GUPTA (BLACK BOOK)-LIMIT-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
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  7. If f (x) = lim ( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of...

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  8. lim(n->oo)cos^2(pi(3sqrt(n^3+n^2+2n)-n)) where n is an integer,equals

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  9. If alpha,beta in (-pi/2,0) such that (sin alpha+sinbeta)+(sinalpha)/(s...

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  10. Let f(x)={|x-2|+a^2-6a+9, x < 2 and 5-2x, x >= 2 If lim(x->2) [f(x)] e...

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  11. A circular disk of unit radius is filled with a number of smaller circ...

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  13. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

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  14. A certain function f(x) has the property that f(3x)=alpha f(x) for all...

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  15. A certain function f (x) has the property that f (3x)=alpha f (x) for ...

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  16. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  17. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  18. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  19. For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...

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  20. Ror the curve sin x+ sin y=1 lying in the first quadrant there exists ...

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