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

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

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Determine the value of the constant k so that the function f(x) = {:{(...

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  2. Find the values of a and b such that the function defined by f(x){(5,"...

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  3. Show that the function defined by f(x) = cos(x^2) is a continuous func...

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

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  5. Examine if sin |x| is a continuous function.

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

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  7. Differentiate the following functions with respect to x. sin(x^3 + 5x)

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  8. Differentiate the following functions with respect to x. cos(sinx)

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  9. Differentiate the following functions with respect to x. sin (a x + ...

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

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

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

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  13. Differentiate the following functions with respect to x. 2sqrt(cot (...

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

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

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  16. Prove that f(x) = [x], 0 lt x lt 3 is not differentiable at x = 1 but ...

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

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  18. Find dy/dx in the following : 2x +3y = sin y

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  19. Find dy/dx in the following: ax + by^2 = cos y

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

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