Need help correcting my final paper before its due, and special help with circled questions! Thank you

3. Perform the following integrals. Show your substitutions and any other work that is needed. a. J 3 + 2VX-4x-' +2e2x_ _ - 1 + x 2 + sin 2x dx [Eax + Sa(x)" dx - [ 4 x"ax + SQex - Sxz, dix + Sinax ax 5 2 x 2 + X' 3/2 - 4 Palx1 + exx _ tan' (x ) - Cos( 2X ) + C b . ( 1 + x)2 dx ( u-sub ) u = ( 1 + * ) X = U - 1 du = d x - 2+1 ) - 2nlul + c = (1+x ) - (1+x ) - 2 n/ 1+ x ) + c C. x2 (1 - x 2)2 dx (Trig. Sub) X X = Sinu 1 - X 2 dx = Cosudu Sin Zu . Cosu du Sinu . Gosh du = ( sinzu du= 1- Cos( 20 ) 1 - Sin zu Cos zu E du - cos ( 24 ) du = 2 Sin (2x ) + C = 4 d. tan-'xdx (Parts) u = tan'x V = X Z = 1+x2 dz = 2xdx U. V - v.du du: - dz - Xdx 1+ x 2 dv= 1 2 = tan 'x . X - Itxz . Xdx = x tan'x - ) X dx = X tun " ' x - z z dz = X tan' x - z In ( z ) + ! 7n . . Divergent = + . 42 72 t ... Convergent SumCalculus II Final Exam Name Gavin Abraham Please show your work. Partial credit is given if work is shown. No Work, No Credit! 1. Differentiate the following. a. f(t) = In(sint) + tan-'t- e* + 5t-1 f(E ) = 1. Cost + 17/2 b. g(x) = xsinx q'(x) = In(qxx> = fa ( x sinx ) Sint 12 - et ( zt ) + 5("zz ) Incgcks ) = Sink lacks f(t) Cost + - 2tet - 5t Sint + 1+t 2 ix In (geos ) = = / Sinx In(x ) F ( t) = Cot (t ) + -- 2tet?- 5t2 9 ( x) . g'( x ) = Sink Inexs + Prix fix Sink 9 ( x) = x sink ) Sinx + Inx . Cosx ] 2. Determine the followng limits. If the limit does not exist, then say so. X a. lim xe -x b. lim 1- cosX * moved gay to otherside x-0* X - Sin x Him X = Jim Sin x X-0 = Nim ox - lim 1 - Cosx 010 X-0 him Cosx x - 0+ Sinx him Cotx = 00 = 0 x -0+ i- Cosx Does Not X-Sinx Exist c. lim Vn + 1 n->co d. lim 1+2 X u = e = him (n+ 1 ) ( 1 + 5 ) * = en ( 1 + 5 x u = e h ( 1+ 8 ) = Him In ( Itn ) X 1 - e = * In ( 1 + 5 ) In ( Ith ) =P = 1 lim Rx ( 1 + 8 ) - 1 = e = -5 Mm/ = 05 S- 5