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

If `f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2)sin(x-x^2)sin2x0sin2x^2|,t h e n` `f(-2)=0` (b) `f^(prime)(-1/2)=0` `f^(prime)(-1)=-2` (d) `f^(0)=4`

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If (1+x)^n=C0+C1+C2\ x^2+\ dot+Cn\ x^n , using derivatives prove th...

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  2. If f,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(x...

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

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  5. Evaluate ("Lim")(x->0)(xcosx-"ln"(1+x))/(x^2)

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  6. Evaluate find a and b if \ ("Lim")(x->0)(x(1+acosx)-bsinx)/(x^3)=1

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  7. ("Lim")(x->0)(e^xsinx-x-x^2)/(x^2+x-"ln"(1-x))

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  8. Evaluate: ("Lim")(x->0)(1+sinx-cosx+"ln"(1-x))/(xtan^2x) -1/2 (b)...

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  9. Evaluate: ("Lim")(x->0)((log)(secx/2)(cosx))/((log)(secx)(cos(x//2))) ...

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  10. Evaluate: ("Lim")(x->1)(x^x-x)/(x-1-lnx)

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  11. Evaluate: ("Lim")(x->0)(1-cosx cos2x cos3x)/(x^2)

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  12. Evaluate: ("Lim")(x->0)((cosa x)^(1//m)-(cosb x)^(1//n))/(x^2)

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  13. Evaluate: ("Lim")(x->0^+)("c o s e c"x)^(1/(lnx))

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  14. Evaluate: ("Lim")(x->pi//2)(secx)^(cotx)

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  15. Evaluate: ("Lim")(x->0^+)(cotx)^(1/(lnx))

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  16. Evaluate: ("Lim")(x->0)(1/x)^(tanx)

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  17. Evaluate: ("Lim")(x->0)x^x

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  18. Evaluate: ("Lim")(x->1)(1-x^2)^(1/(ln(1-x)))

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  19. Evaluate: ("Lim")(x->4)(sqrt(2x+1)+sqrt(x-3)-4)/(sqrt((3x+4))+sqrt(5x+...

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  20. Evaluate ("Lim")(x->pi/2)tanxlogsinx using Lhospitals Rule

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