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Discuss the continuity of fx) at x =0, w...

Discuss the continuity of fx) at x =0, when:
`f(x) = {:{((e^(1//x) -1)/(e^(1//x)+1),xne0),(0,x=0):}`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If f(x) = {:{(xsin(1/x),xne0),(0,x=0):} Show that 'f' is not different...

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  2. Show that the function defined by: f(x) : {:{(3-2x,ifx<2),(3x-7,ifxg...

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  3. Discuss the continuity of fx) at x =0, when: f(x) = {:{((e^(1//x) -1...

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  4. Show that the function: f(x) = {:{(2+x,ifxge0),(2-x,ifx<0):} is cont...

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  5. Show that the function 'f' defined as follows, is continuous at x = 2,...

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  6. The function 'f' defined as: f(x) = {:{(x^2+3x+a,ifxle1),(bx+2,ifx>1...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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