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If f(x) = {{:(b([x]^(2)+[x])+1",","for",...

If `f(x) = {{:(b([x]^(2)+[x])+1",","for",x gt -1),(sin(pi(x + a))",","for",x lt -1):}`, where [x] denotes the integral part of x, then for what values of a, b, the function is continuous at x = - 1?

A

`a = 2n + (3)/(2), b in R, n in I`

B

`a = 4n + 2, b in R, n in I`

C

`a = 4n + (3)/(2), b in R^(+), n in I`

D

`a = 4n + 1, b in R^(+), n in I`

Text Solution

Verified by Experts

The correct Answer is:
A, C
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (More Than One Correct Option Type Questions)
  1. On the interval I=[-2,2], the function f(x)={{:(,(x+1)e^(-((1)/(|x|)+(...

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  2. Given f(x)={{:(3-[cot^(-1)((2x^3-3)/(x^2))], x >0) ,({x^2}cos(e^(1...

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  3. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x gt -1),(sin(pi(x + a))",","f...

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  4. Find dy/dx if y= x/tanx

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  5. If f(x) = |x+1|(|x|+|x-1|), then at what point(s) is the function not ...

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  6. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

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  7. If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} th...

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  8. f(x) = cos x and H(x) = {{:(min{f(t), 0 le t lt x},0 le x le (pi)/(2))...

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  9. If f(x) = 3(2x + 3)^(2//3) + 2x + 3, then: (a) f(x) is continuous but ...

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  10. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

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  11. if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} ...

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  12. Let [x] denote the greatest integer less that or equal to x. If f(x) =...

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  13. The function f(x)=x-[x] , where [⋅] denotes the greatest integer fu...

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  14. The function f(x)=sqrt(1-sqrt(1-x^2)) a. has its domain -1 le x le 1 ...

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  15. Consider the function f(x) = |x^(3) + 1|. Then,

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  16. f is a continuous function in [a,b]; g is a continuous function in [b,...

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  17. Which of the following function(s) has/have the same range ?

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  18. If f(x) = sec 2x + cosec 2x, then f(x) is discontinuous at all points ...

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  19. Show that f(x)={{:("x sin"(1)/(x)",","when",x ne 0),(0",","when",x = 0...

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  20. A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0)...

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