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The function defined by f(x)={((|x-3),, ...

The function defined by `f(x)={((|x-3),, x ge 1), (1/4x^2-3/2x+13/4,, x lt 1):}` is

A

continuous at x=1

B

Continuous at x=3

C

Differentiable at x=1

D

all of these

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The correct Answer is:
D
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. The function f(x)=|x|atx=0 is:

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  2. g(x)=x|x|theng''(x)

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  3. The function defined by f(x)={((|x-3),, x ge 1), (1/4x^2-3/2x+13/4,, x...

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  4. If f(x)={((x-1)/(2x^2-7x+5), for x ne 1),(-1/3, for x=1):} then f(1)=

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  5. Let h(x)=max{-x,1,x^2} for every real x, then number of points of non-...

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  6. lim(nrarrinfty)(n^ksin^2n!)/(n+1)=0 for

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  7. If f(x)=sin(2pi[pi^2x])/(5+[x^2]) denotes the greatest integer functio...

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  8. If f(x)=|x-25| and g(x)=f(f(x)) then for xgt50, g'(x) is equal to

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  9. Let f(x)=[tan^2x], where [.]denotes the greatest integer function. The...

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  10. If f(x+y)=f(x). f(y) for all x and y and f(5)=2, f'(0)=4, then f '(5) ...

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  11. if f(x)=[sqrt2sinx], where [x] denotes the greatest integer function, ...

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  12. f(x)=[x]+|x-1| then f(x), where [.] denotes greatest integer function)...

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  13. If f(x)={(-x, x le 1),(3+x, x gt1):}, g(x)= {(x^2, x le 1),(2-x,x gt 1...

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  14. If {x} denotes the fractional part of x, then lim(xrarr0)(e^{x}-1)/x i...

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  15. Consider f(x)={(x^2/|x|, x ne 0),(0, x=0):}

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  16. Value of lim(x rarr 3)(sin(e^(x-3) -1))/log(x-2) is

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  17. lim(x rarr 1) x^(1//1-x) is

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  18. lim(x rarr 0) ((1+tan x)/(1-tan x))^(1/x) is

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  19. The value of lim(x rarr 0) (int0^(x^2)sec^2tdt)/(x sinx) is :

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  20. The value of lim(x rarr 0) |cosx + sinx|/x^2 is equal to

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