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Let f: R rarr R(R is the set of real num...

Let `f: R rarr R`(R is the set of real numbers) be defined as follows:
`f(x) = { : (2-x , if 1lexle2),(x-1/2x^2 ,if x ge 2) :` Examine the continity and differentiability of f(x) at x=2.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. The function 'f' defined as: f(x) = {:{(x^2+3x+a,ifxle1),(bx+2,ifx>1...

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  2. For what values of 'a' and 'b' the function: f(x) = {:{(x^2,xlec),(a...

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  3. Let f: R rarr R(R is the set of real numbers) be defined as follows: ...

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  4. Show that f(x) = |x-3|, x in R is continuous but not differentiable at...

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  5. Write an example of a function, which is continuous everywhere but fai...

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  6. Use Chain Rule to find the derivatives of the following: f(x) = (1-2...

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  7. Find the derivatives of the following: f(x) =(x^2+3x+4).

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  8. Use Chain Rule to find the derivatives of the following: f(x) = (3x^...

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  9. Use Chain Rule to find the derivatives of the following: f(x)=(2x^2+...

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  10. Use Chain Rule to find the derivatives of the following: f(x)=3/(2-x...

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  11. Find the derivatives of the following: h(x) = (x+1)(x+2)(x+3)

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  12. Use Chain Rule to find dy/dx, if y = ((3x-1)/(3x+1)^2)

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  13. Find dy/dx, if y = (4x^3 - 5x^2+1)^

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  14. Find dy/dx, if y = 1-2((5x)/(3x+2))^2 +((5x)/(3x+2))^3

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  15. Differentiate the following w.r.t. x: sin(x^2)

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  16. Differentiate the following w.r.t. x: sin(x^2+5)

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  17. Differentiate the following w.r.t. x: tan(3x+5)

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  18. Differentiate the following w.r.t. x: sinx^0

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  19. Differentiate the following w.r.t. x: sin^4(ax+b)^2

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  20. Differentiate the following w.r.t. x: sin(cotx)

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