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Find the value of a for which the following function is continuous at a given point. `f(x)={xsin(1/x ),\ x!=0 and a ,\ x=0`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
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  7. Find the value of a for which the following function is continuous ...

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  8. If f(x)={(x-4)/(|x-4|)+a ,\ \ \ if\ x<4a+b ,\ \ \ if\ x=4(x-4)/(|x-4|)...

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  9. If f(x) is continuous in (-oo, 6), where f(x)={: {(1+sin ((pi x)/(2))...

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  10. The value of a and b such that the function f(x) {:{(-2 sin x", ...

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  11. Value of f(0) so that f(x) = (log(1+bx)-log(1-ax))/x is continuous at...

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  12. The value of f(0), so that the function f(x)=(sqrt(a^2-a x+x^2)-sqrt(...

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  13. Let f(x)=lim(n->oo)(log(2+x)-x^(2n)sinx)/(1+x^(2n)). then

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  14. Discuss the continuity of f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)),x!=1,2 6,x=...

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  15. If the function and the derivative of the function f(x) is everywhere ...

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  16. If the function f(x)=(3x^2+a x+a+3)/(x^2+x-2) continuous at x=-2.find...

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  17. Find all possible values of a and b so that f(x) is continuous for all...

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  18. The function f(x) = [{:((6/5)^(tan 6x)/(tan 5x), if, 0 lt x lt pi/2),(...

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  19. Suppose that f(x)=x^3-3x^2 and h(x) =[(f(x))/(x-3), x!=3 then K , ...

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  20. Let yn(x)=x^2+(x^2)/(1+x^2)+(x^2)/(1+x^2)^2+...(x^2)/(1+x^2)^(n-1) and...

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