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

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

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate: ("Lim")(x->1)(x^x-x)/(x-1-lnx)

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

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

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

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

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

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

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

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

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

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

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  12. Evaluate ("Lim")(x->0)(logcosx)/x using Lhospitals Rule

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  13. Evaluate ("Lim")(x->0)(2^x-1)/((1+x)^(1//2)-1) using Lhospitals Rule

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  14. Evaluate ("Lim")(x->pi/4)(2-tanx)^(1/(ln(tanx))) using Lhospitals Rule

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  15. If ("Lim")(x->a)(a^x-x^a)/(x^x-a^a)=-1 and a >0 , then find the value ...

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  16. f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim(x->oo)f(x) is equal...

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  17. Let f(x+y)=f(x)f(y) for all x and y . Suppose f(5)=2 and f^(prime)(0)=...

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  18. Let f(x y)=f(x)f(y)\ AA\ x ,\ y in R and f is differentiable at x=1 s...

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  19. If f((x+2y)/3)=(f(x)+2f(y))/3\ AA\ x ,\ y in R and f^(prime)(0)=1 , f...

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  20. If f is twice differentiable such that f^(x)=-f(x) and f^(prime)(x)=g(...

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