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If lim(x->0)(1+a x+b x^2)^(2/x)=e^3, th...

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

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

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

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

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

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  8. Evaluate: ("lim")(xvec1)("sin"{x})/({x}) if exists, where {x} is the f...

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

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  10. Evaluate: ("lim")(nvec0)(1^(1//sin^2x)+2^(1//(sin^2x))++n^(1//sin^2x))...

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  11. Let f(x)={cos[x],xgeq0|x|+a ,x<0 The find the value of a , so that (...

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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&lt;1 and ax ,1lt=x&lt;2 If lim(x->1)f(x) e...

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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 (a) -pi (b) pi (c) ...

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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 (a) e (b) e^(-1) ...

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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")(xvecoo){1/(1-n^2)+2/(1-n^2)+......n/(1-n^2)}i se q u a lto 0 ...

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