46. [-/1 Points] DETAILS MY NOTES LARCALC12 4.R.074. ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the integral using the properties of even and odd functions as an aid. (cos( x ) + * 6 ) dx Need Help? Read It Submit Answer 47. [-/1 Points] DETAILS MY NOTES LARCALC12 4.R.501.XP. ASK YOUR TEACHER PRACTICE ANOTHER Find the indefinite integral. (Remember the constant of integration.) * + 12 dx x5 Need Help? Read It Submit Answer 48. [-/1 Points] DETAILS MY NOTES LARCALC12 4.R.502.XP. ASK YOUR TEACHER PRACTICE ANOTHER Find the indefinite integral. (Remember the constant of integration.) (7 cos( x ) - 6 sec 2 ( x ) ) dx Need Help? Read It Submit Answer 49. [-/1 Points] DETAILS MY NOTES LARCALC12 4.R.503.XP. ASK YOUR TEACHER PRACTICE ANOTHER Find the particular solution of the differential equation that satisfies the initial conditions. f"(x) = 4 cos(x), f'(0) = 2, f(0) = -7 f( x ) = Need Help? Read It (Submit Answer 50. [-/1 Points] DETAILS MY NOTES LARCALC12 4.R.504.XP. ASK YOUR TEACHER PRACTICE ANOTHER Use the Fundamental Theorem of Calculus to evaluate the definite integral. Use a graphing utility to verify your result. [* Vxox51. [-/1 Points] | DETAILS | MY NOTES LARCALC12 4.R.505.XP. ASK YOUR TEACHER PRACTICE ANOTHER Use the Fundamental Theorem of Calculus to evaluate the definite integral. Use a graphing utility to verify your result, 51 f ( + X) dx 1 X3 Need Help? Submit Answer 52. [-/1 Points] DETAILS MY NOTES LARCALC12 4.R.506.XP. ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the definite integral. Use a graphing utility te verify your result. 1 4 [ (y+ 11 ydy 0 Need Help? [Emasanng] 53. [-/4 Points] DETAILS MY NO LARCALC125.1.015. [ ASK YOUR TEACHER H PRACTICE ANOTHER ] Use the properties of logarithms to approximate the indicated logarithms, given that In(2) = 0.6931 and In{3) = 1.0986. {a) In(6) 3 (b) In(z) {c) In(16) (d) |n() Need Help? Submit Answar 54. [-/1 Points] LARCALC125.1.018. ASK YOUR TEACHER PRACTICE ANOTHER Use the properties of logarithms to expand the logarithmic expression. |"'( v\"?) [ ] Need Help? [ Submit Answer | 55. [-/1 Points] DETAILS MY NOTES LARCALC125.1.023. I ASK YOUR TEACHER H PRACTICE ANOTHER l Use the properties of logarithms to expand the logarithmic expression. |n( \\,/) :_ Write the expression as a logarithm of a single quantity. %(4 In{x + 6) + In{x) In{x2 EJ} Need Help? [[lRssani)] [ Submit Answer | 57. [-/1 Points] DETAILS MY NOTES LARCALC12 5.1.037. [ ASK YOUR TEACHER H PRACTICE ANOTHER l Find the limit. (Round your answer to four decimal places. If the limit is infinite, enter '=' or "-=', as appropriate. If the limit does not otherwise exist, enter DNE.) lim |n(x2[9 - x)) x 8" Need Help? 58. [-/1 Points] DETAILS MY NOTES LARCALC12 5.1.041. ASK YOUR TEACHER PRACTICE ANOTHER Find the derivative of the function. f(x) = In(x% + 7) Frix) = ' Need Help? [ Submit Answer | 59. [-/1 Points] DETAILS MY NOTES LARCALC12 5.1.045. [ PRACTICE ANOTHER l ASK YOUR TEACHER Find the derivative of the function. y = In{(t + 8)%) - | Need Help? Submit Answer 60. [-/1 Points] DETAILS MY NOTES LARCALC12 5.1.052. ASK YOUR TEACHER PRACTICE ANOTHER Find the derivative of the function. In(t} t9+6 hit) = h'(t) =