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Discuss the continuity of the function f...

Discuss the continuity of the function f defined by
`f(x)={(x+2,"if",x lt 1),(x-2,"if",x gt 1):}`

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To discuss the continuity of the function \( f \) defined by: \[ f(x) = \begin{cases} x + 2 & \text{if } x < 1 \\ x - 2 & \text{if } x > 1 \end{cases} ...
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NCERT-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES
  1. If y=sin^(-1)x, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0.

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  2. Find all the points of discontinuity of the function f defined byf(x)=...

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  3. Discuss the continuity of the function f defined by f(x)={(x+2,"if",x...

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  4. Discuss the continuity of the function f given by f(x)={x , ifxgeq0x^2...

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  5. Discuss the continuity of the function defined byf(x)={x+2, ifx<0-x+2,...

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  6. Find all the points of discontinuity of the greatest integer function...

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  7. Show that every polynomial function is continuous.

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  8. Discuss the continuity of sine function.

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  9. Prove that every rational function is continuous.

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  10. Show that the function defined by f(x) = sin(x^2)is a continuous func...

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

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  12. Examine whether the function f given by f(x)=x^2 is continuous at x =...

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  13. Discuss the continuity of the function f given by f(x) = |x| at x = 0.

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  14. Check the continuity of the function f given by f(x) = 2x + 3 at x = ...

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  15. Prove that the identity function on real numbers given by f(x) = x is...

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  16. Is the function defined by f(x) = |x|, a continuous function?

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  17. Show that the function f given by f(x)={x^3+3ifx!=0 ;1ifx=0 is not ...

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  18. Check the points where the constant function f(x) = kis continuous.

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  19. Discuss the continuity of the function/given by f(x)=x^3+x^2-1.

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  20. Discuss the continuity of the function f defined by f(x)=1/x , x!=0.

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