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f:[0,\ 1]->R is defined as f(x)=[x^3(1-x...

`f:[0,\ 1]->R` is defined as `f(x)=[x^3(1-x)sin(1/(x^2))\ \ \ if\ 0

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. The function f: RvecR satisfies f(x^2)dotf^(x)=f^(prime)(x)dotf^(prime...

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  2. Let f(x)=[x e^x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xlt=0x+x^2-x^...

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  3. f:[0,\ 1]->R is defined as f(x)=[x^3(1-x)sin(1/(x^2))\ \ \ if\ 0<xlt=1...

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  4. Let f: R->R satisfying f((x+y)/k)=(f(x)+f(y))/k( k != 0,2).Let f(x...

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  5. Let (f(x+y)-f(x))/2=(f(y)-a)/2+x y for all real xa n dydot If f(x) is ...

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  6. If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...

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  7. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

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  8. Evaluate ("Lim")(x->0)[1/(x^2)-1/(sin^2x)] using LHospitals Rule or ot...

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  9. Evaluate ("Lim")(x->0)(1+sinx-cosx+ln(1-x))/(x tan^2x) using LHospital...

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  10. If ("Lim")(x->0)(asinx-b x+c x^2+x^3)/(2x^2dotln(1+x)-2x^3+x^4) exists...

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  11. Evaluate: ("Lim")(x->0)(x^(6000)-(sinx)^(6000))/(x^2dot(sinx)^(6000))

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  12. If lim(x->0)(1-cosx.cos2x.cos3x ....cosn x)/x^2 has the value equal to...

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  13. Find the value of ("Lim")(x->0)(1-cos^5xcos^3 2xcos^3 3x)/(x^2)

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  14. If ln(x+y)=2x y , then y '(0)?

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  15. f(x)={bsin^-1((x+c)/2),-1/2 lt xlt0 and 1/2 , x=0 and e^(((ax)/2)-1)/...

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  16. If y=y(x) and it follows the relation xcosy+ycosx=pi then y''(0) is

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  17. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

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  18. If f(x) is a continuous and differentiable function and f(1/n) = 0 ...

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  19. The value of lim(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is ...

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  20. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2...

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