Find the Taylor's series expansion for `log(cos x) `about the point` (pi)/(3) `

The series expansion of log{(1+x)^(1+x)(1-x)^(1-x)} is

Find the coefficient of x^(3) in the power series expansion of (5x+6)/((x+2)(1-x)) specifying the region in which the expansion is valid.

Find the number of solutions to log_(e) |sin x| = -x^(2) + 2x in [-(pi)/(2), (3pi)/(2)] .

Evaluate the limits using the expansion formula of functions lim_(x->0) (sinx+log(1-x))/x^2

If the third term in the expansion of (1/x+""_"x"(log)_(10 x))^5 is 1000 , then find xdot

Find is the coefficient of x^(4) in the power series expansion of (3x^(2)+2x)/((x^(2)+2)(x-3)) specifying the interval in which the expansion is valid.

Find the co-efficient of x^(2) in the expansion of (x + 2)^(6) .

Find the Cartesian co-ordinates of point whose polar co-ordinates are (4, (pi)/(3)) .

Find the coodinates of the point of intersection of the curves y= cos x , y= sin 3x if -(pi)/(2) le x le (pi)/(2)

Find the value of x satisfying the equation ((log)_3 root(3)(3x)+(log)_x root(3)(3x))dot(log)_3x^3+((log)_3 root(3)(x/3)+(log)_xroot(3)(3/x))dot(log)_3x^3=2