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Evaluate: ("lim")(x to oo)((a1^( 1/x)+a2...

Evaluate: `("lim")_(x to oo)((a_1^( 1/x)+a_2^ (1/x)+ --+a_ n^(1/x))/n)^(n x)`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If lim(x->0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,where theta...

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  2. If L=lim(x->0)(sin2x+asinx)/(x^3) is finite, then find the value of ...

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  3. Evaluate: ("lim")(x to oo)((a1^( 1/x)+a2^ (1/x)+ --+a n^(1/x))/n)^(n x...

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  4. Evaluate: ("lim")(xrarr0)(sinx^0)/x

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  5. Evaluate: ("lim")(xto0)(1-"cos"(1-cosx)dot)/(x^4)

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  6. Evaluate: [("lim")(xrarr0)(tan^(-1)x)/x], where [.]represent the g...

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  7. Let f(x)={x+1,x >0 \n 2-x ,xlt=0 and g(x)={x+3,x<1,x^2-2x-2,1lt=x<2x...

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  8. Evaluate: ("lim")(xto pi/4)(sqrt(2)cosx-1)/(cotx-1)

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  9. lim(x->0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the gre...

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  10. Evaluate: ("lim")(xvec0)(1-cosm x)/(1-cosn x)

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

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

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

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

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  15. lim(x-&gt;0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)= (a)-1 (b) ...

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

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

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

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

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