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F(x) is the function such that (lim)(x...

`F(x)` is the function such that `(lim)_(x->0)(f(x))/x=1\ a n d\ (lim)_(x->0)(x(1+acosx))/((f(x))^3)=1` , then find the value of `a`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. lim(x rarr oo) (sqrt(x^2-x+1)-a x-b)=0, then a+b=

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  2. If lim(x -> oo) (1 + a/x + b/x^2)^(2x)= e^2 then the values of a and ...

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  3. F(x) is the function such that (lim)(x->0)(f(x))/x=1\ a n d\ (lim)(x...

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  4. If Sn=sum(k=1)^n ak and lim(n->oo)an=a , then lim(n->oo)(S(n+1)-Sn)/sq...

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  5. (lim)(x->oo)(logx^n-[x])/([x]),\ n in N ,\ ([x]\ d e not e s\ t h e\ ...

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  6. (lim)(x->-2)(sin^(-1)(x/4)\ )/(x^2+2x) is equal to...............

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  7. If (lim)(x->0)(log(3+x)-"log"(3-x))/(x^2-9)="k", then the value of...

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  8. The value of (lim)(x->oo)2/x"log"(1+x) is equal to............

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  9. The value of lim(x->0^+) x^m (logx)^n, m,n in N is

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  10. lim(n->oo) 1/sqrt(n^2)+1/sqrt(n^2+1)+1/sqrt(n^2+2)+.....1/sqrt(n^2+2n)...

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  11. Using Sandwich theorem, evaluate lim(n->oo)(1/(1+n^2)+1/(2+n^2)+.........

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  12. lim(hrarr0)(sin(pi/3+4h)-4sin(pi/3+3h)+6sin(pi/3+2h)-4sin(pi/3+h)+sinp...

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  13. Evaluate the following limits: lim(xto0)(sin4x)/(6x)

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  14. Evaluate the following limit: (lim)(x->0)(e ^(x^2)-3^(3x))/(sin((x^2...

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  15. lim(x->-oo)((3x^4+2x^2)sin(1/x)+|x|^3+5)/(|x|^3+|x|^2+|x|+1)

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  16. Evaluate the following limit: (lim)(x->1/(sqrt(2)))(cos^(-1)(2xsqrt...

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  17. (lim)(xvec-7)([x]^2+15[x]+56)/("sin"(x+7)"sin"(x+8))= (where [.] denot...

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  18. Evaluate the following limit: (lim)(x->(3pi)/4)(1-tan3x)/(1-2cos^2x)

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  19. Evaluate: ("lim")(nvec0)8/(x^8){1-cos(x^2)/2-cos(x^2)/4+cos(x^2)/2cos(...

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  20. Evaluate the limit: ("lim")(xvec1)(sumk=1 100 x^k-100)/(x-1)

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