3. (10 points) Find the Taylor series for the function f(x) = er centered at a = 2. f ( n ) = 2 f" (a ) ( x - a)n ph ( a ) = ea a = 2 po ( 2 ) = e ' f ( x ) = = =2 ( n- 2) 2 ney n!For problems 4 and 5, determine the slope of the tangent line to the curve at the indicated point. If the slope is undefined, state that it is undefined. fermog Al 4. (10 points) x = 4 + sin(t), y = t cos(t), t = 1/4 12 = cost . =4 ( - sint ) + cost dx = ces (t ) de dy = cost - + sint de dy ( ay ldt) cost - t sint d x (dx loft ) cost 2x ) = 1 - t tan (t ) dy = 1- Fly 5. (10 points) r = 3(1 + cos(20)), 0 = 1/2 dy dy since Ox dir case- rsing do = since (3 ( - 0 120 ) . 2) + 3 ( 1 + (c) 20) coco 3 (-smore ). zcesc +- (sci + ceszo)ance at 9= ah 8 ll /2)(-68 na) + 3(1+cuz( ) cence 8 (- 8a) . 2040 7 +-(3 (1+ (OBx ) sin (7/2) not defined because at @= 1/2, 1= 02. (10 points) 2" ( x - 1 ) n W n=1 Radius of convergence R = 1Im an an = nano antl R = lim 2n (n+ 1 ) ! = tim (n+ 1)1 2n = lim = limn (n+ 1 ) it converges overall real number.For problems 1 and 2, determine the interval of convergence for the indicated power series. 1. (10 points) (-1)"(x - 3)n n = 1 radius of conv" R = interval of convergence sub ( an ) 'n an = ( - 1)n 1x- 31