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If lim(xrarr0)(1+ax+bx^2)^(2//x)=e^3, th...

If `lim_(xrarr0)(1+ax+bx^2)^(2//x)=e^3`, then the value of a and b, is :

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Find the value of alpha so that lim(x->0)1/(x^2)(e^(alphax)-e^x-x)=3/...

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  2. If x(1) and x(2) are the real and distinct roots of ax^(2)+bx+c=0 then...

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  3. If lim(xrarr0)(1+ax+bx^2)^(2//x)=e^3, then the value of a and b, is :

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

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

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  6. Evaluate: lim(x->0)(e^x-1-x)/(x^2)

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  7. If ("lim")(x to0)(a e^x-b)/x = 2 , then find the value of a and bdot

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  8. Evaluate: ("lim")(xto1)("xsin"{x})/({x-1}) if exists, where {x} is the...

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  9. Evaluate: lim(x->2) (x^2-1)/(2x+4)

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  10. Evaluate: ("lim")(xto0)(1^(1//sin^2x)+2^(1//(sin^2x))++n^(1//sin^2x))^...

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  11. Let f(x)={{:(cos[x]", "xle0),(|x|+a", "xgt0):}. Then find the value...

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  12. If f(x)=|x-1|-[x], \where\ [x] is the greatest integer less then or eq...

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  13. If y=2^(-2^((1/(1-x))) , then find lim(x->1^+)y

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  14. Let f(x)={1+(2x)/a ,0lt=x<1 and ax ,1lt=x<2 If lim(x->1)f(x) exists ,...

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  15. Evaluate ("lim")(x->0) (sinx-2)/(cosx-1)

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  16. lim(xrarr0)sin(picos^2x)/x^2 is equal to :

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  17. Evaluate lim(x->0^-) (x^2-3x+2)/(x^3-2x^2)

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  18. For x in R, lim(xrarroo)((x-3)/(x+2))^x is equal to

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  19. Evaluate lim(n-&gt;oo) [sum(r=1)^n1/2^r] , where [.] denotes the gre...

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  20. lim(n->oo){1/(1-n^2)+2/(1-n^2)+......n/(1-n^2)} is equal to (a) 0...

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