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`f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):}` Discuss the continuity

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To determine the continuity of the piecewise function \( f(x) \) defined as: \[ f(x) = \begin{cases} 2x & \text{if } x < 0 \\ 0 & \text{if } 0 \leq x \leq 1 \\ 4x & \text{if } x > 1 ...
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NCERT ENGLISH-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.1
  1. f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):}...

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  2. Find all points of discontinuity of f, where f is defined byf(x)={{:(...

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  3. Find all points of discontinuity of f, where f is defined byf(x)={{:(...

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  4. Find all points of discontinuity of f, where f is defined byf(x)={{:(...

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  5. Is the function f defined byf(x)={{:(x , ifxlt=1),( 5, ifx >1):}conti...

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  6. Prove that the function f(x)=x^nis continuous at x = n, where n is a ...

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  7. Find all points of discontinuity of f, where f is defined byf(x)={{:(...

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  8. Find all points of discontinuity of f, where f is defined byf(x)={{:(...

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  9. Prove that the function f(x) = 5x-3is continuous at x = 0, at x =-3and...

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  10. Examine the following functions for continuity. (a) f(x)=x-5 (b) f(x...

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  11. Examine the continuity of the function f(x)=2x^2-1at x = 3.

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  12. For what value of lambdais the function defined by f(x)={{:(lambda(x^...

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  13. Show that the function defined by g (x) = x [x] is discontinuous at ...

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  14. Discuss the continuity of the function f, where f is defined byf(x)={...

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  15. Find the relationship between a and b so that the function f defined ...

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  16. Discuss the continuity of the function f, where f is defined byf(x)={...

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  17. Is the function defined by f(x)={{:(x+5, ifxlt=1),(x-5, ifx >1):} a c...

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  18. Find all points of discontinuity of f, where f is defined byf(x)={{:(...

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  19. Find all points of discontinuity of f, where f is defined byf(x)={{:(...

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  20. Find the values of k so that the function f is continuous at the indi...

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