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Prove that every rational function is co...

Prove that every rational function is continuous

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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Textbook Illustrations for Practice Work
  1. Show that every polynomial function is continuous.

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

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  3. Prove that every rational function is continuous

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  4. Discuss the continuity of sine function

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  5. Prove that the function defined by f(x)= tan x is a continuous functio...

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

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  7. Show that the function f defined by f(x)= |1-x + |x|| where x is any r...

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  8. Find the derivative of the function given by f(x)= sin x^(2)

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  9. Find the derivative of tan (2x + 3)

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  10. Differentiate sin(cos x^(2)) with respect to x

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  11. Find (dy)/(dx) if x-y= pi

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  12. Find (dy)/(dx) if y+ sin y= cos x

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  13. Find the derivative of f given by f(x)= sin^(-1)x assuming it exists.

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  14. Find the derivative of f given by f(x)= tan^(-1)x assuming it exists

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  15. Is it true that x= e^(log x) for all real x?

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  16. Differentiate the following w.r.t x: (i) e^(-x) (ii) sin (log x), x ...

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  17. Differentiate sqrt((x-3) (x^(2) + 4))/sqrt((3x^(2) + 4x + 5)) w.r.t x.

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  18. Differentiate a^(x) w.r.t x, where a is a positive constant

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  19. Differentiate x^(sin x), x gt 0 w.r.t x

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  20. Find (dy)/(dx), If y^(x) + x^(y) + x^(x)= a^(b)

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