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Prove that the function f defined by f(x...

Prove that the function f defined by `f(x) = {((x)/(|x|+ 2x^(2))",","if" x ne 0),(k,"if" x = 0):}` remains discontinuous at x=0, regardless the choice of k

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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-NCERT Exemplar Problems and Solution (Short Answer Type Questions)
  1. Find the values of k so that the function f is continuous at the indic...

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  2. Find the values of k so that the function f is continuous at the indic...

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  3. Prove that the function f defined by f(x) = {((x)/(|x|+ 2x^(2))",","if...

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  4. Find the values of a and b such that the function f defined by f(x) ...

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  5. If the function f(x)= (1)/(x+2), then find the points of discontinuity...

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  6. Find all points of dicontinuity of the function f(t)= (1)/(t^(2) + t-2...

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  7. Show that the function f(x)= |sinx + cos x| is continuous at x= pi

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  8. Examine the differentiability of f, where f is defined by f(x) = {(x...

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  9. Determine if f defined by f(x) = {(x^(2)"sin" (1)/(x)",","if" x ne 0),...

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  10. Examine the continuity of the function f(x)= {(1+x",","if " x le 2),(5...

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  11. Show that f(x) = |x-5| is continuous but not differentiable at x= 5

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  12. A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for ...

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  13. Differentiate 2^(cos^(2)x)

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  14. Differentiate (8^(x))/(x^(8))

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  15. Differentiate log (x + sqrt(x^(2) + a))

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  16. Differentiate the following with respect to x: log [log (log x^(5))]

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  17. Differentiate sin sqrtx + cos^(2) sqrtx

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  18. Differentiate sin^(n) (a x^(2) + bx + c)

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  19. Differentiate cos (tan sqrt(x+ 1))

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  20. Differentiate sin x^(2) + sin^(2)x + sin^(2) (x^(2))

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