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("lim")(xvecoo)"{"(n/(n+1))^(alpha)+s in...

`("lim")_(xvecoo)"{"(n/(n+1))^(alpha)+s in1/n"]"^n(w h e nalpha in Q)i se q u a lto` `e^(-alpha)` (b) `-alpha` (c) `e^(1-alpha)` (d) `e^(1+alpha)`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. If f(x)=("lim")(xvecoo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equa...

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  2. The value of ("lim")(xvec2)(2^x+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))i s ...

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  3. ("lim")(xvecoo)"{"(n/(n+1))^(alpha)+s in1/n"]"^n(w h e nalpha in Q)i ...

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  4. Let f(x)=("lim")(xvecoo)1/((3/pitan^(-1)2x)^(2n)+5)dot Then the set of...

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  5. ("lim")(xvec0){(1+x)^(2/x)} (where {.} denotes the fractional part of ...

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  6. lim(x->0) sin(x^2)/(ln(cos(2x^2-x)) is equal to

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  7. If f(x)={x^nsin(1/(x^2)),x!=0 0,x=0,(n in I),t h e n ("lim")(xvec0)...

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  8. (lim)(x->0)((1^x+2^x+3^x++n^x)/n)^(1/x)\ is equal to (n\ !)\ ^n b. (n...

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  9. Among (i) ("lim")(xvec0)sec^(-1)(x/(sinx))a n d(i i i)("lim")(xvecoo)s...

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  10. If ("lim")(xvec0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n m...

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  11. ("lim")(xvec1)((1-x)(1-x^2)(1-x^(2n)))/({(1-x)(1-x^2)(1-x^n)}^2),n in ...

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  12. The value of ("lim")(xvec0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] ...

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  13. If ("lim")(xvec0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n m...

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  14. If ("lim")(xvec0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, th...

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  15. For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q ...

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  16. ABC is an isosceles triangle described in a circle of radius r.If AB=...

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  17. Let f be a differentiable function on the open interval(a, b). Which o...

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  18. If f(x) = |1 -x|, then the points where sin^-1 (f |x|) is non-differen...

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  19. Let f(x)=1/(1+e^(1/x))for\ x!=0\ a n d\ f(0)=0 , then f(0^+) does not ...

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  20. Let f(x)=[(sinx)/x]+[(2sin2x)/x]++[(10sin10 x)/x] (where [.] is the gr...

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