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Discuss the continuity of the function ...

Discuss the continuity of the function
`f(x)={((|x|)/x", " xne 0),(1", " x=0):}` at x=0

A

` x gt 0`

B

` x lt 0`

C

0

D

None of these

Text Solution

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The correct Answer is:
C
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NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Exercies 5o
  1. Discuss the continuity of the function f(x)={((|x|)/x", " xne 0)...

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  2. Prove that the function defined by f(x) = t a n xis a continuous func...

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  3. The function f(x)= {(2 ax ", " x le 3 ),( 3x +1 ", " x gt 3):}...

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  4. The function f(x)={sinx/x +cosx , x!=0 and f(x) =k at x=0 is continuo...

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  5. The function f(x)= {(5x-4 ", " 0 lt x le 1 ),( 4x^3-3x", " 1 l...

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  6. Show that the function f(x)=2x-|x| is continuous at x=0 .

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  7. The value of 'k' for which f(x)= {(kx^2", " x ge 2 ),(12", ...

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  8. The value of k for which f(x)= {((1-cos 2x )/(x^2 )", " x ne 0 ),(...

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  9. If the function f(x)= {(3ax +b", " x gt 1 ),(11 ", "x=...

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  10. The value of 'a' for which f(x)= {((sin^2 ax)/(x^2)", " x ne 0 ),(...

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  11. If y= sin ^-1\ (1)/(sqrt(1+x^2)) then dy/dx at x =0 is :

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  12. If y=(x)/(x+5), then prove that x (dy)/(dx) = y(1 - y)

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  13. If x^y=e^(x-y) , then (dy)/(dx) is (1+x)/(1+logx) (b) (1-logx)/(1+logx...

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  14. If y= tan ^-1 ((x)/sqrt(a^2-x^2)) then dy/dx =?

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  15. If y= tan^-1((1-x)/(1+x))+cot^-1((1-x)/(1+x)) then dy/dx= ?

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  16. If y=sin^(-1)((1-x^2)/(1+x^2)) , then (dy)/(dx)= -2/(1+x^2) (b) 2/(1+...

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  17. If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s x/(2y-1)...

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  18. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to tan^(-1)((2...

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  19. If f(x)= x^2+7x+10 then f'(2) =?

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  20. At which point the slope to tangent is zero for the curvey y=x^2-6x+8 ...

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