Please answer all the questions thoroughly. I've provided the answer key below.

MATH 1325 - Test 5 Review - Dave Rice Sections 12.7, 7.1, 7.2, 7.4 Use L'Hospital's Rule to evaluate the limit. 1) lim Xz - 9 x -3 X- 3 Objective: (12.7) Use L'Hospital's Rule to Find Limit I 2) lim 2ex -2x - 2 x - 0 x2 Objective: (12.7) Use L'Hospital's Rule to Find Limit I Find the integral. 3) [x5 dx Objective: (7.1) Find Indefinite Integral by Power, Constant Multiple Rules 4 ) [ 10 dx Objective: (7.1) Find Indefinite Integral by Power, Constant Multiple Rules 5 ) [4x2/3 dx Objective: (7.1) Find Indefinite Integral by Power, Constant Multiple Rules 6) [ dx Objective: (7.1) Find Indefinite Integral by Power, Constant Multiple Rules 7) [(8x2 + 1) dx Objective: (7.1) Find Indefinite Integral by Power, Sum/Difference Rules 8) [ (3x8 - 7x3 + 4) dx Objective: (7.1) Find Indefinite Integral by Power, Sum/Difference Rules 9 ) 8ety dy Objective: (7.1) Find Indefinite Integral of Exponential Function 10 ) J[ # + 2ex ) ax Objective: (7.1) Find Indefinite Integral of 1/x11) 2. Objective: (7.1) Find Indefinite Integral of 1/x 12 ) x5 + 1 dx Objective: (7.1) Find Indefinite Integral of 1/x Use substitution to find the integral. 13 ) 4 ( 2x + 5) 3 dx Objective: (7.2) Use Substitution to Find Indefinite Integral I 14 ) [V6x - 7 dx Objective: (7.2) Use Substitution to Find Indefinite Integral I 15 ) [ (y - 1)7 dy Objective: (7.2) Use Substitution to Find Indefinite Integral I 16) 10e4x dx Objective: (7.2) Use Substitution to Find Indefinite Integral of Exp Function 17) 19 2 + 5y dy Objective: (7.2) Use Substitution to Find Indefinite Integral II 18 ) ( (In x) ax X Objective: (7.2) Use Substitution to Find Indefinite Integral of Log Function Evaluate the definite integral. 19 ) J wv x dx A) 32 B) 48 ( ) -64 D) 8 Objective: (7.4) Evaluate Definite Integral I 20) " Tex dx Objective: (7.4) Evaluate Definite Integral I21 ) ( x2 + x+ 3) dx -3 Objective: (7.4) Evaluate Definite Integral II 22 ) x-1/2 dx Objective: (7.4) Evaluate Definite Integral II 23 ) [ ( x +3) dx Objective: (7.4) Evaluate Definite Integral II 24 ) ( 4x + 2)(5x - 1) dx Objective: (7.4) Evaluate Definite Integral III 25 x - - dx Objective: (7.4) Evaluate Definite Integral III Use substitution to evaluate the definite integral. 26) [ Ax 3 ext ax A) 4e B) 4e - 1 C)e- 1 D) e Objective: (7.4) Evaluate Definite Integral Using Substitution 27 ) [ x ( x 2 + 1) 5 dx Objective: (7.4) Evaluate Definite Integral Using Substitution 28 ) ( x - 3 ) 3 dx Objective: (7.4) Evaluate Definite Integral Using SubstitutionAnswer Key Testname: 1325 TEST 5 REVIEW 1) lim x2 - 9 32 - 9 0 x - 3 x- 3 3-3 0 - ==> use L'Hospital's Rule: lim X- - 9 _ lim 2x_2(3) -6 x - 3 x- 3 x - 31 2) lim 2ex - 2x - 2 _2e -2(0) - 2 2(1) - 0 -2 _0 x - 0 x2 02 0 0 - ==> use L'Hospital's Rule: lim 2ex - 2x - 2 - lim 2ex - 2 _2e2(0) - 2 _2(1) - 2 0 X - 0 x2 x - 0 2x 2(0) 0 - ==> use L'Hospital's Rule again: lim 2ex - 2 = lim 2ex X - 0 2x - = lim 20 2(1) =1 x -0 2 x - 0 2 2 Thus, lim 2ex - 2x - 2 = 1 x - 0 x2 3) x6 + C 4) 10x + C 5) 12x5/3 + C 6) - 22 + C 7) 2x3 + x + C 8 ) - x9 - - x4 + 4X + C 9) 2e4y + C 10) 4 In | x| + 2ex + C 11) In |x - 23 x 2x2 12) -x5 + In /x| + C 13 ) = ( 2 x + 5 ) 4 + C 14 ) - ( 6 x - 7) 3/2 + C 15 ) - (y - 1)8 + C 16) 34 17) - In |2 + 5y| + CAnswer Key Testname: 1325 TEST 5 REVIEW 18) (In x) 10 10 19) C 20) 7e2 - 7 21) 10.67 22) 2 23) 10.5 184 25) 20 26) C 27) 1302 28) - - 81 4 29) e2 - e 30) In 4 31) AFind the area of the shaded region. 29) X Objective: (7.4] Find Area of Shaded Region 31) Hint: Set x3 4x = 0 and solve for x t0 find the value of x where it intercepts the xaxis. Objective: (7.4] Find Area of Shaded Region