IIT JEE , AIEEE Forum - Mathematics , Algebra

suryasivateja

1. log(1-x+x^2) is expressed as sum of infinte series in ascending powers of x,what is the coefficient of x^9...

2.The area of the equilateral triangle inscribed in the circle x^2 + y^2 -2x = 0

3.lim x------> infinity e^(1/x^2)/(2Tan-1 X -pi)

4. The circumference of the triangle formed by the points (3,-1,2) (1,2,-3) & (2,-3,-1)

shakirshafi12

i cant type them too lengthy

see this

shakirshafi12

as for 3rd question well e^(1/x^2) tends to one when x tends to infinity and denominator tands to zero

titun

Hiii,

ANS:1) log (1-x+x^2) = log[(1+x^3)/(1+x)] = log(1+x^3) - log(1+x)

= x^3 - x^6 / 2 + x^9 / 3 - [x - x^2 / 2 + x^3/3 - .......... ]

The coefficient of x^9 in the expansion is 1/3 - 1/9 = 2/9

ANS:2) Find the radius of the circle. Since, the circle is the circumcircle of an equilateral triangle, the radius of the circle, r = 2/3 a, where a is the altitude of the equilateral triangle. Area of an equilateral triangle = a^2/

3 sq units

= 3

3/4 x r^2 sq. units.

Radius of the circle can be calculated from the given data & hence the reqd. area of the triangle can be found out.

The questions 3 & 4 is not very clear to me. I don't understand what have been written in question no. 3. Is the entire thing in the exponent of e?

In the last question, Are we to find the circumference of the circumscribing circle or the perimeter of the triangle ?

Anyways, I hope the solutions of the other two problems satisfy you.

Cheers !!!

vinu

Hi,

2 ) radius=r=1,

Area of equi triangle =h²/

3;

and 2h/3=r

Area =3

3/4.

{titun,u messed up with 'a' , a bit}

shakirshafi12

ya even i had got area same as vinu

v_gurucharan

Q 4.

circumfrence= approx 15.5 units

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