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Show that the function f defined by f(x)...

Show that the function f defined by `f(x)= |1-x + |x||` where x is any real number is continous.

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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Textbook Illustrations for Practice Work
  1. Prove that the function defined by f(x)= tan x is a continuous functio...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Find (dy)/(dx), if x = a cos theta, y= a sin theta

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  18. Find (dy)/(dx), if x= a t^(2), y= 2 a t

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  19. Find (dy)/(dx), if x= a (theta + sin theta), y= a (1- cos theta)

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  20. Find (dy)/(dx), if x^((2)/(3)) + y^((2)/(3))= a^((2)/(3))

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