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("lim")(xvec1)((1-x)(1-x^2)(1-x^(2n)))/(...

`("lim")_(xvec1)((1-x)(1-x^2)(1-x^(2n)))/({(1-x)(1-x^2)(1-x^n)}^2),n in N ,e q u a l s` `^2n P_n` (b) `^2n C_n` (c) `(2n)!` (d) none of these

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lim_(x rarr1)((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^(2)),n in N, equals ^2nP_(n)(b)^(2n)C_(n)(c)(2n)!(d) none of these

Evaluate: int e^(x)(1+nx^(n-1)-x^(2n))/((1-x^(n))sqrt(1-x^(2n)))dx

lim_(x rarr2)((1+x)^(n)-3^(n))/(x-2)=n*3^(n-1)

lim_(x rarr oo){(1)/(1-n^(2))+(2)/(1-n^(2))+(n)/(1-n^(2))} is equal to 0 (b) -(1)/(2)(c)(1)/(2)(d) none of these

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

lim_(x rarr0^(-))([x]+[x^(2)]+[x^(3)]++[x^(2n+1)]+n+1)/(1+[x^(2)]+|x|+2x),n in N

If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e r en in N , then value of a is n b. n-1 c. n+1 d. none of these

The value of lim_(x->oo)((2^(x^n))^(1/e^x)-(3^(x^n))^(1/e^x))/(x^n) (where n in N) is (a)logn(2/3) (b) 0 (c) nlogn(2/3) (d) none of defined

lim_(x rarr oo)n^(2)(x^((1)/(n))-x^((1)/((n+1)))),x>0, is equal to (a)0(b)e^(x)(c)(log)_(e)x(d) none of these

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Among (i) ("lim")(xvec0)sec^(-1)(x/(sinx))a n d(i i i)("lim")(xvecoo)s...

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

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

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

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

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

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

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

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

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

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  13. In a quadratic equation ax^2 + bx+c= 0 if 'a' and 'c' are of opposite ...

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  14. Let f(x)""=""x|x|""a n d""g(x)""=""s in x Statement 1 : gof is diff...

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  15. Statement 1:(lim)(x->0)sin^(-1){x}\ does not exist (where {.} denot...

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  16. Statement 1: lim(x->0) sqrt(1-cos 2x)/x does not existe . Statement 2...

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  17. Statement 1: If f(x)={x ,\ if\ x\ i s\ irr a t ion a l1-x ,\ if\ x\ i ...

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  18. Statement 1: (lim)(x->0)[x]((e^(1//x)-1)/(e^(1//x)+1)) (where [.] repr...

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  19. Statement 1: The function f(x)=[[x]]-2[x-1]+[x+2] is discontinuous ...

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  20. Let f(x)=-ax^2-b|x|-c, -alpha le x lt 0, ax^2+b|x|+c 0 le x le alpha ...

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