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Prove that lim(xrarroo)(1+1/x)^x=e...

Prove that `lim_(xrarroo)(1+1/x)^x=e`

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 3-EXERCISE
  1. Show that the distance between (1,-1) and ((2m^2)/(1+m^2),(1-m)^2/(1+m...

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  2. Find the radius of sphere passing through (2,0,1) and having centre(0,...

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  3. Prove that lim(xrarroo)(1+1/x)^x=e

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  4. For all real values of x and y, if f(x+y)=f(x)f(y), f(5)=4, f'(0)=2, f...

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  5. IfP(A)=1/2,P(B)=1/3)and P(A capB)=1/4find (A 'capB')

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  6. In.an examination. 50%of the condidates have passed in mathematics 50%...

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  7. If A,B,(A - B)are positive acute angles, then prove that geometrically...

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  8. Show thatcos((2pi)/7)+cos((4pi)/7)+cos((6pi)/7)=-1/2

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  9. Show that a^6+a^4+a^2+1=0,when a=1/sqrt2(1+i)

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  10. Prove by mathematical induction:(3^(4n+1)+2^(2n+2))is divisible by 7.

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  11. Show that the co-efficient of the middle term of the expansion of(1+x)...

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  12. If (y/z)^a.(z/x)^b.(x/y)^c=1and a,b,c are in A.P ,show that x,y,z are ...

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  13. In /\XYZthe equation of the perpendicularbisector of XY and XZ arc x-y...

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  14. Find the distance of the point (3. 5) from the line 2x + 3y = 14measur...

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  15. The end’ points of a rod having length l are moving a long with two st...

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  16. Find the equation of a circle .which passes through (-2. 1) and touche...

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  17. Evaluate:lim(x-0)((e^x-1)log5(1+5x))/(sin^2x)

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  18. Differentiate a^x with respect to x (a> 0) with the help 1st principle...

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  19. ‘I80 is the multiple of 4 or 5 examine the validity of the compound st...

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  20. ‘x is such a real number that 4x^3 + 3x= 0, then x = O’. Find the trut...

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