please explain them on papers with pen so i can understand

For the given rectangular equation, write an equivalent polar equation. 56) 5x - 3y - 8 =0 A) r 8 5 cos 0 - 3 sin 0 B) 12 = 8 5 cos 0 - 3 sin 0 8 C) r: 5 sin 0 - 3 cos 0 5 sin 0 - 3 cos 0 D)r = 10 For the given polar equation, write an equivalent rectangular equation. 57) r = 5cot 0 esc 0 B) y = 5x2 D) y2 =5x A) y = 5x C) y = Graph the polar equation. 3 58) r = sin 0 6 rFind the quadratic approximation of fat x = 0. 40) f(x) = esin 2x A) Q(x) - 1 + 2x + 2x2 B) Q(x) - 2x - 2x2 C) Q(x) = 2x + 2x2 D) Q(x) = 1 - 2x + 2x2 41) f(x) = sin In(7x + 1) A) Q(x) = 7x - - 49 x2 2 ' B) Q(x) = 7x + -x2 C) Q(x) = 1 - 7x + 49 2 -x2 D) Q(x) = 1 +7x + =x2 2 Find the first four nonzero terms in the Maclaurin series for the function. 42) f(x) = In (1 + x3 A) 1 3_ 16 +1,9 1 -x 12 B) x3 1 12 + 3 67 12 24 C) x3 -1x6 + 1,9. D) 6 +. x 12 + 2 6 24 3For what values of x does the series converge conditionally? 36) (7x)n n=0 A ) x = B) x =0 C) x =-7 D) None Find the Maclaurin series for the given function. 37) 4 + X A) S (-1)n xn .4n+1 B) (in xn n=0 n=0 4n C) " (In xn+1 4n D) (-1)n xn n=0 4n+1 38) e7x 18 A) (-1)n zn xn n! B) (-1)n 7n xn iM 8 n=1 n=0 n! 7n xn C 2 7n xn n! D) > n=1 n! n=0 Find the Taylor series generated by f at x = a. 39) f(x) = e4x, a -8 A) e32 4n+1 (x - 8)n B) e32 4n (x - 8)n n=0 n! n=0 (n + 1)! e32 4n+1 (x - 8)n e32 4n (x - 8)n (n + 1)! D) n! n=04n+1 20) n=1 8n-1 A) Converges; 8 B) Converges; 32 C) Converges; 64 D) Diverges Find the values of x for which the geometric series converges. 21) > (x -6)n n=0 A) 5