I need help Cal 2 Please

MATH 1326 FINAL Mock EXAM FALL 2024 Final Exam is 2hours 15 mins. This is not expected to be finished during class time. (1) (a) (5 points) Find the derivative of, (i) f(x) = In(e212 + 3x) (ii) f(ac) = e-323+12+5 (b) (5 points) Evaluate the following limits. If you are using a Theorem, please name it. (i) lim 2et + In (x + 1) - 2 (3.x2 + e2x - 1) (ii) lim (2) (10 points) Evaluate the following integrals. (a ) 6x2 + 12x (23 + 3x2+ 1) dx ( b ) x(2 - Inx)2 dx e27 + 1 (C ) - dx (3) (10 points) For the curves given by f(x) = 2x3 + 2x2 + x+ 1, g(x) = x3 +2x2 + x + 9 and interval [0, 4]. (a) (2 points) Find where the curves intersect. (b) (2 points) Find which curve is above and which is below by some means inside [0, 2] interval. (c) (6 points) Write down the correct integrals with the correct limits to find the area enclosed between these two curves. (4) (10 points) (a) (5 points) Integrate. 1 ) (x2 + x) Inedx bros (b) (5 points) For the improper integrals below, determine if it converges or diverges and find its value if it converges. Note that there will be (i) for writing it using the proper notation for improper integral, (ii) for correct integration, and (iii) for correctly showing convergence or divergence. 1 (i) (1 + 2x)2 dx (ii) 1 + 22 dx