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Evaluate: lim(x->0)(tan2x-x)/(3x-sinx)...

Evaluate: `lim_(x->0)(tan2x-x)/(3x-sinx)`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate: ("lim")(xvec0)(1-cosm x)/(1-cosn x)

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  2. lim(x->oo)cot^(-1)(x^(-a)loga x)/(sec^(-1)(a^xlogx a)),(a >1)is equal ...

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  3. Evaluate: lim(x->0)(tan2x-x)/(3x-sinx)

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  4. The value of ("lim")(xveca)sqrt(a^2-x^2)cot(pi/2)sqrt((a-x)/(a+x)) is ...

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  5. Evaluate: ("lim")(xvec0)(cot2x-cos e c2x)/x

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  6. lim(x->0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)= (a)-1 (b) ...

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  7. Evaluate: (lim(n->oo)ncos(pi/(4n))sin(pi/(4n))

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  8. The value of lim(n->oo)[(2n)/(2n^2-1)cos(n+1)/(2n-1)-n/(1-2n)dot(n(-1)...

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  9. Evaluate: ("lim")(hvec0)(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(sqrt(3)h(...

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  10. Evaluate: ("lim")(xrarr0)8/(x^8){1-cos((x^2)/2)-cos((x^2)/4)+cos((x^2...

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  11. Evaluate: ("lim")(xvec0)(cos^(-1)((1-x^2)/(1+x^2)))/(sin^(-1)x)

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  12. Evaluate:lim(n->oo)n{sqrt((1-cos(1/n))sqrt((1-cos(1/n))sqrt((1-cos(1/n...

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  13. Evaluate: ("lim")(x→0,y→0)(y^2+sinx)/(x^2+siny^2) where (x , y)→(0,0)...

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  14. Evaluate ("lim")(n→oo){cos(x/2)cos(x/4)cos(x/8)... cos(x/(2^n))}

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  15. Find the value of alpha so that lim(x->0)1/(x^2)(e^(alphax)-e^x-x)=3/...

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  16. If x1 and x2 are the real and distinct roots of a x^2+b x+c=0, then ...

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  17. If lim(x->0)(1+a x+b x^2)^(2/x)=e^3, then find the value of a and b.

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  18. Evaluate: ("lim")(n→oo)x[tan^(-1)((x+1)/(x+2))-tan^(-1)(x/(x+2))]

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  19. If ("lim")(xvecoo){(x^2+1)/(x+1)-(a x+b)}=0, then find the value of aa...

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  20. Evaluate: ("lim")(xto0)(e^x-1-x)/(x^2), without using LHospitals rule...

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