Precalculus First Semester Review
18) Use change of base to approximate the following to three decimal places π) log! 216 π) log! 91 π₯π¨π πππ π₯π¨π π
= π.πππ π₯π¨π πππ₯π¨π π
= π.πππ 19) Evaluate the following limits π) lim!β!
!!!!!!!"!!!
π) lim!β!! !!! !!! !!!!
!
π) lim!β!
!!!! !!
π) lim!β!!!
!!!!!!!
20) A certain population (in thousands) grows according to the equation π = 40π!.!"#!
where P represents the population and t represent the number of years since 2000. a) Determine the year when the population 60 thousand will be reached. ππ = ππππ.ππππ π.π = ππ.ππππ π₯π§ π.π = π.ππππ π = π₯π§ π.π
π.πππ= ππ.πππ πππππ
ππππ b) Determine the population in 2003 π· π = ππππ.πππ(π) = ππ.πππ ππ ππ,πππ c) Determine the initial population. ππ,πππ 21) Given π΄ = 1 0
3 4 and π΅ =β3 20 3
a) Find 3π΄ + π΅ b) Find AB d) Find π΄!! 22) Given the geometric sequence with π! = 32 and π = !
!
a) Write the formula π! for the sequence
ππ = ππ ππ
π!π
b) Write the first five terms of the sequence ππ,ππ,π,π,π c) Determine the term π!"
πππ = ππ ππ
ππ!π= π
ππ
Precalculus First Semester Review
23) Given the arithmetic sequence with π! = 20 and π = β3 a) Write the formula π! for the sequence ππ = βππ+ ππ b) Write the first four terms of the sequence ππ,ππ,ππ,ππ c) Determine the term π!" πππ = βπ ππ + ππ = βπ 24) Determine the value of the account with an initial balance of $3000 that is compounded quarterly with an interest rate of 8% after 5 years.
π¨ = ππππ π+ .πππ
π π= ππππ.ππ
25) Determine the value of an account with an initial balance of $3000 that is compounded continuously with an interest rate of 8% after 5 years. π¨ = πππππ.ππ(π) = ππππ.ππ 26) Determine the coefficient of the following terms in the expansion of 3π₯ + 6π¦ ! a) π₯!π¦! b) π₯!π¦ ππππ ππππ 27) Evaluate the following a) πΆ! ! b) πΆ! ! c) πΆ! ! 28) Write in a + bi form: !!!!
!!!!
π!πππ!ππ
π!πππ!ππ
= π!ππ!πππ!πππ
π!πππ= π!πππ!π
π!π= !π!πππ
ππ= β π
ππ+ πππ
ππ
29) Graph the function and tell whether or not it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-Ββremovable. a) π π₯ = !
! b) π π₯ = !!!!
!
non-Ββremovable removable
Precalculus First Semester Review
30) Simplify a) log!! 11! b) ln !
! c) log!
!!"
π βπ βπ 31) Find the zeros of the function algebraically. a) π π₯ = 3π₯! + 2π₯ β 5 b) π π₯ = π₯! β 36π₯ πππ + ππβ π = π ππ β πππ = π ππ+ π πβ π = π π ππ β ππ = π π = β π
π,π π πβ π π+ π = π
π = π,βπ,π 32) Determine whether the functions are even, odd, or neither a) π π₯ = 3π₯! β 2π₯ b) π π₯ = 2π₯! β 3π₯! + 5 ODD EVEN 33) Do the following functions have an inverse? If so, find it a) π π₯ = π₯! + 1! b) π¦ = 2 β π₯ π = ππ + ππ π = πβ π ππ = ππ + π ππ = πβ π ππ β π = ππ π = πβ ππ π = ππ β π 34) Divide !
!!!!!!!!
with long division 35) Divide !!!!!!!!!!!!
with synthetic ππ + ππ+ π πππ β πππ + ππβ πβ π
π!π
36) Where is the following function discontinuous? a) π¦ = !!!
!!! b) π¦ = !
!!!!!!!
π = π π = βπ,βπ