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If the function f(x) defined by {:(f(x...

If the function f(x) defined by
`{:(f(x),=x (sin)1/x,",","for"x != 0),(,=k, ",","for"x = 0):}`
is continuous at x = 0, then k =

A

0

B

1

C

`-1`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
A
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TARGET PUBLICATION-CONTINUITY-Competitive Thinking
  1. If the function f(x) = {((x^(2)-(A+2)x+A)/(x-2), ",", x != 2),(2, ",",...

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  2. The value of k which makes f(x) = {((sin(1/x)), ",", x != 0),(k, ","...

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  3. If the function f(x) defined by {:(f(x),=x (sin)1/x,",","for"x != 0)...

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  4. If f(x) = {(ax^(2)-b, ",", "when" 0 le x le 1),(2, ",","when"x = 1),(x...

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  5. If f(x) = {(sin x, ",", "if" x le 0),(x^(2)+a^(2), ",", "if" 0 lt x l...

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  6. If f(x) = {((1-sinzx)/(pi-2x), ",", x != pi/2),(lambda, ",", x = pi/2...

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  7. If a function of defined by f(x) = {((1-sinzx)/(pi-2x), ",","if" x != ...

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  8. Let f(x) = {((tan x - cot x)/(x-pi/4), ",", x != pi/4),(a, ",", x = p...

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  9. if f(x)=sin[x]/([x]+1) , x > 0 and f(x)=(cospi/2[x])/([x]) , x < 0 and...

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  10. The function defined by f(x) = {((x^(2)+e^(1/(2-x)))^(2), ",",x != 2...

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  11. If f(x) = (log(e)(1+x^(2)tanx))/(sinx^(3)), x != 0 is continuous at x ...

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  12. The function f: R-{0} -> R given by f(x)=1/x-2/[e^2x-1] can be made co...

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  13. If {:(f(x),=(20^x + 3^x - 6^x- 10^x)/(1-cos 8x),",","for"x != 0),(,=(k...

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  14. If f(x) = {((x-2)/(|x-2|)+a, ",",x lt2),(a+b, ",", x = 2 ),((x-2)/(|x-...

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  15. If f(x) = |x|+|x-1|, then

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  16. If f(x) = {((x^(2)-4x+3)/(x^(2)-1), ",","for"x != 1),(2, ",", "for"x =...

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  17. If f(x) = {((|x-a|)/(x-a), ",","when"x != a),(1, ",", "when"x = a ):} ...

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  18. The function f(x) = |x| = (|x|)/x is

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  19. The points of discontinuity of the function f(x)=(2x^(2)+7)/(x^(3)+3x...

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  20. If f: R to R is defined by f(x) = {(x-1, ",","for"x le 1),(2-x^(2),...

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