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Examine the function, f(x)={(x-1, x lt...

Examine the function, `f(x)={(x-1, x lt 0),(1//4, x=0), (x^2-1, xgt 0):}`
Discuss the continuity, and if discontinuous remove the discontinuity.

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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f(x)={({1+|sinx|}^(a//|sinx|), -pi//6ltxlt0),(b, x=0),(e^(tan2x...

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  2. Discuss the continuity of f(x)=[tan^(-1)x]

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  3. Examine the function, f(x)={(x-1, x lt 0),(1//4, x=0), (x^2-1, xg...

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  4. Show the function, f(x)={((e^(1//x)-1)/(e^(1//x)+1), "when x" le 0),...

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  5. A function f(x) is defined by, implies f(x)=f(x)={(([x^2]-1)/(x^2-1)...

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  6. Discuss the continuity of the function, f(x)=lim(nrarrinfty)(log(2+x)...

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  7. Discuss the continuity of f(x) where f(x)=lim(nrarrinfty)("sin" (pix)/...

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  8. If f(x) be continuous function for all real values of x and satisfies,...

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  9. Which of the following functions is differentiable at x=o ?

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  10. Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x)...

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  11. Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x)...

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  12. The left hand derivative of f(x)=[x]sin (pix) at x=k, k is an integer,...

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  13. A function f:R rarr R satisfies the equation f(x+y)=f(x)f(y) for all x...

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  14. Let f(x)={(-4, -4 lexlt0),(x^2-4, 0lexle4):} Discuss the continuity a...

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  15. Let f(x)=[n+p sin x], x in (0, pi) n in Z and p is a prime number, whe...

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  16. If f(x)={|x|-|x-1|}^2, draw the graph of f(x) and discuss its continui...

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  17. If f(x)=|x+1|{|x|+|x-1|}, then draw the graph of f(x) in the interval ...

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  18. The value of lim(xrarr0)(int0^(x^2) cos(t^2)dt)/(xsinx) is

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  19. The value of lim(xrarr0)(1^x+2^x+3^x+...+n^x)^(a//x)/n, is:

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  20. If lim(xrarr0)(1+ax+bx^2)^(2//x)=e^3, then the value of a and b, is :

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