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If f(x)={:{(x", for " 0 le x lt 1),(2", ...

If `f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x le 2):}`, then f is

A

f is continuous at `x=1`

B

f is discontinuous at `x=1`

C

`underset(x rarr 1^(-))lim f(x)=2`

D

`underset(x rarr 1^(+))lim f(x)=1`

Text Solution

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The correct Answer is:
B
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NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
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  2. If f(x)={:{((sin2x)/(sqrt(1-cos2x))", for " 0 lt x le pi/2),((cos x)/(...

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  3. If f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x...

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  4. If f(x)=(x^(3)+3x+5)/(x^(3)-3x+2) in [0, 5], then f is

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  5. If f(x)=(x+1)/((x-2)(x-5)), then in [4, 6]

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  6. If f(x)=(x+1)/((x-2)(x-5)), then in [0, 1]

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  7. If f(x)={:{(x", for " x ge 0),(x^(2)", for " x lt 0):}, then f is

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  8. If f(x)={:{(x^(2)-4", for " 0 le x le 2),(2x+3", for " 2 lt x le 4),(x...

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  9. If f(x)={((1)/(x+1)", for " 2 le x le 4),((x+1)/(x-3)", for " 4 lt x l...

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  10. If f(x)={:{(3", if " 0 le x le 1),(4", if " 1 lt x lt 3),(5", if " 3 l...

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  11. If f(x)={:{(-2", for " x le -1),(2x", for " -1 lt x le 1),(2", for " x...

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  12. f(x)={(|x|+3",","if", x le -3),(-2x",", "if", -3 lt x lt 3),(6x+2",","...

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  13. If f(x)={(2x", for " x lt 0),(2x+1", for " x ge 0):} , then

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  14. Function f(x)={(x-1",",x lt 2),(2x-3",", x ge 2):} is a continuous fun...

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  15. If f(x)=(x^(3)-8)/(x^(2)+x-20), then

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  16. If f(x)={:{((x^(2)-3x+2)/(x-3)", for " 0 le x lt 4),((x^(2)-1)/(x-2)",...

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  17. If the function f(x)=k +x, "For" x lt1 =4x+3, "For" x ge1 is co...

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  18. If f(x) is continuous at x=0, where f(x)={:{(x^(2)+1", for " x ge 0),...

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  19. If f(x) is continuous at x=0, where f(x)={:{(k(x^(2)-2)", for " x le ...

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  20. If f is continuous at x=0 , where f(x)=x^2+alpha ,x>=0, f(x)=2sqrt(...

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