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A function f(x) is defined by, implies...

A function f(x) is defined by,
`implies f(x)=f(x)={(([x^2]-1)/(x^2-1) "for" x^2ne1),(0 "for"x^2=1):}`
Discuss the continuity of f(x) at x=1.

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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  7. Which of the following functions is differentiable at x=o ?

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

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

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

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

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

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

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

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  19. A function is defined as, f(x)={(0, where x is rational),(1, where x ...

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  20. If f(x)={(-1, xlt0 ),(0, x =0),(1, x gt 0):} and g(x)=x(1-x^2), then...

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