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Examine the continuity of the function '...

Examine the continuity of the function 'f' at x = 0, if `f(x) ={(x sin(1/x)),(0):}, ((x ne 0),(x = 0))

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PSEB-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. Show that the function defined by f(x) = cos(x^2) is a continuous func...

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  2. Show that the function defined by f(x) = |cosx| is a continuous functi...

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  3. Examine the continuity of the function 'f' at x = 0, if f(x) ={(x sin(...

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  4. Find all the points of discontinuity of f defined by f(x) = |x|-|x+1|

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  5. Differentiate the functions with respect to x: sin(x^2 + 5)

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  6. Differentiate the functions with respect to x: cos(sinx)

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  7. Differentiate the functions with respect to x: sin(ax+b)

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  8. Differentiate the functions with respect to x: sec(tan(sqrtx))

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  9. Differentiate the functions with respect to x: (sin(ax+b))/(cos(cx+d))

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  10. Differentiate the functions with respect to x: cos x^3 cdot sin^2 (x^5...

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  11. Differentiate the functions with respect to x: 2sqrt(cot(x^2))

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  12. Differentiate the functions with respect to x: cos(sqrtx)

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  13. Prove that the function f given by f(x) = |x-1|, x in R, x=1 is not di...

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  14. Prove that the greatest integer function defined by f(x) = [x], 0<x<3,...

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  15. Find dy/dx in the following: 2x+3y= sinx

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  16. Find dy/dx in the following: 2x+3y= siny

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  17. Find dy/dx in the following: xy+y^2= tanx +y

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  18. Find dy/dx in the following: x^2+xy+y^2= 100

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  19. Find dy/dx in the following: x^3+x^2y+xy^2+y^3=81

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  20. Find dy/dx in the following: sin^2y + cosxy = k

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