please show all work neatly. for final exam. Thanks so much

lim X-1 Evaluate the limit In ( x ) lim 3 x 2 + X 2 Evaluate the limit ( 2X -1 ) 2 3 Evaluate the limit lim xox 4 Find Ist derivative , Please simplify answer if possible y= x In ( 9 x 2 ) 5 find Ist derivative . Simplify if possible sing (3 x ) 6 find Ist derivative . Simplify if possible y = sin? (5 x ) tan ( x3) 7 y = x 3 sin ( 2 x ) Find Ist derivative , simplify if possible 8 f ( x ) = ( x 3 + 2 x ) e 3 X And Ist derivative , simplify if possible 9 find equation of the tangent line to the given curve at the given ( x ) -value y = ( 3 x + 1 2 when * = 1 find the second derivative . Please simplify if possible y = 2x X2 - 411. you want to design a pen to hold your Vietnamese pis . The penis to be split into 3 areas of equal size , with the seperating fences all running parallel . If you have 100 meters of fencing , Answer the following questions write the equation you need to use to maximize the area - write out the constraints for the problem what are the outside dimensions of the pen ? by ? 12 Let In denote the left-endpoint SUM using I subintervals and let Rn denote the corresponding right endpoint sum . Given the following function and interval : f ( x ) = 1 from * = - 2 to * = z x 2+1 a - calculate Ry to approximate the area under the curve b - find the exact area under the curve by evaluating an appropriate definite integral 13. v ( + ) = 4+3 + 3 sin't" And the position function find the acceleration of object when + = 014 evaluate the integral dx X 15 evaluate the integral x d x 16 evaluate the integral ( COS() + ( * ) ) dix