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mathematics
precalculus

Questions and Answers of Precalculus

For the functionfind f (2) and f (3). f(x) = x - 1 x
Problems 103–112. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 103–112. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
Problems 104 – 113. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 104 – 113. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 103–112. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 1–4, list the first five terms of each sequence. {an} = {(-1)" (n + 2)}
Problems 103–112. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 103–112. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 104 – 113. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Solve the given equation (8) =__and (1) =
In Problems 26–28, use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers. 3 + 6 + 9 + ... + 3n 3п n -(n + 1)
True or False n j! (n − j)!n!
In Problems 1 – 22, use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 3+ 4+ 5+ + (n + 2) = n(n+ .. • /n(n + 5) 5)
If sinθ = 1/4 and θ is in the second quadrant, find: (a) cos (c) sin(20) (e) sin(10) (b) tan 0 (d) cos(20)
In Problems 17 – 28, expand each expression using the Binomial Theorem.(x2 + y2)5 THEOREM Binomial Theorem Let x and a be real numbers. For any positive integer n, + + (²) ₁²x^-1 (x + a)² = (
If |r| < 1, the sum of the geometric seriesis ________. 00 Σαγκ ar k=1 k−1
In Problems 5 – 16, evaluate each expression. 5 3
How much do you need to invest now at 5% per annum compounded monthly so that in 1 year you will have $10,000?
In Problems 15–26, list the first five terms of each sequence. (-1)" {tn} {^₂} = {{m² + (2)} ((n + 1)(n+ 2).
In Problems 22–25, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 2-1+ 2 4 +
In Problems 22–25, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. ++ 016 +
In a(n)_______ sequence, the ratio of successive terms is a constant.
Solve the equation: 2ex = 5
A(n)_______ is a function whose domain is the set of positive integers.
In Problems 15–26, list the first five terms of each sequence. {an} 3n - {²} n
In Problems 15–26, list the first five terms of each sequence. {cn}= n 2n
If a series does not converge, it is called a(n)________ series.(a) Arithmetic(b) Divergent(c) Geometric(d) Recursive
In Problems 17 – 28, expand each expression using the Binomial Theorem. (√x + √2)°
An arithmetic sequence can always be expressed as a(n) sequence.(a) Fibonacci(b) alternating(c) increasing(d) recursive
In Problems 15–26, list the first five terms of each sequence. n {bn} -{} n
In Problems 33 – 40, find the nth term an of each geometric sequence. When given, r is the common ratio. -3, 1, 1 1 ㄎ… 3'9'
Problems 37–45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
In Problems 29 – 42, use the Binomial Theorem to find the indicated coefficient or term.The coefficient of x0 in the expansion of THEOREM Binomial Theorem Let x and a be real numbers. For any
In Problems 23–27, prove each statement.If 0 < x < 1, then 0 < xn < 1.
In Problems 29 – 42, use the Binomial Theorem to find the indicated coefficient or term.The coefficient of x4 in the expansion of THEOREM Binomial Theorem Let x and a be real numbers. For any
In Problems 23–27, prove each statement.a − b is a factor of an − bn. ak+1 − bk+1 = a(ak − bk ) + bk (a − b)
Problems 37–45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
Problems 37–45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.A
Find the partial fraction decomposition of 3x x2 + x - 2 +
Problems 37–45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
In Problems 23–27, prove each statement.(1 + a)n ≥ 1 + na, for a > 0
In Problems 29 – 42, use the Binomial Theorem to find the indicated coefficient or term.The coefficient of x2 in the expansion of THEOREM Binomial Theorem Let x and a be real numbers. For any
In Problems 35–48, a sequence is defined recursively. List the first five terms.a1 = 2; an = 3 + an−1
In Problems 41 – 46, find each sum. 3 + 32 9 + 33 9 + + 3n 9
In Problems 41 – 46, find each sum. 14 2 2² 23 ++ + 4 4 + + 2n-1 4
Renaldo gets paid once a month and contributes $350 each pay period into his 401(k). If Renaldo plans on retiring in 20 years, what will be the value of his 401(k) if the per annum rate of return of
In Problems 35–48, a sequence is defined recursively. List the first five terms.a1 = −2; an = n + an−1
In Problems 35–48, a sequence is defined recursively. List the first five terms. a₁ -2; ann + 3an-1 = = =
In Problems 31–38, find the first term and the common difference of the arithmetic sequence described. Find a recursive formula for the sequence. Find a formula for the nth term.12th term is 4;
In Problems 35–48, a sequence is defined recursively. List the first five terms.a1 = 2; an = −an−1
Problems 37–45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If
In Problems 39–56, find each sum.−1 + 3 + 7 + . . . + (4n − 5)
In Problems 69–80, find the sum of each sequence. 50 k=1 8
Show that (n²1) = n and n n 1.
In Problems 41 – 46, find each sum. 2 + 015 + 18 ·+· 25 ... n-1 + 2(3)
If n is a positive integer, show that2n = (1 + 1)n ; now use the Binomial Theorem. n (1) + + ... + n n 2n
For Problems 47 – 52, use a graphing utility to find the sum of each geometric sequence. بنات + 32 33 + 9 9 + + 315 9
If n is a positive integer, show that n n (6)-(8)+(3) ----+-(C)-· n n 2 . = = 0
In Problems 69–80, find the sum of each sequence. 26 Σ(3κ – 1) 7) k=1
In Problems 69–80, find the sum of each sequence. 40 Σκ k=1 k
In Problems 69–80, find the sum of each sequence. 24 Σ(κ) K=1
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
In Problems 41 – 46, find each sum.− 1 − 2 − 4 − 8 − . . . − (2n−1)
In Problems 69–80, find the sum of each sequence. 20 k=1 (5k + 3) +
Find the inverse of the matrixif it exists; otherwise, state that the matrix is singular. 2 3 0 -1
Suppose {an} is an arithmetic sequence. If Sn is the sum of the first n terms of {an}, and S2n/Sn is a positive constant for all n, find an expression for the nth term, an, in terms of only n
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
In Problems 69–80, find the sum of each sequence. 40 Σ(-3k) k=8
In Problems 69–80, find the sum of each sequence. 20 Σκ k=5 3
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
Find the partial fraction decomposition of 3x x3 - 1
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
Problems 75–84. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 75–84. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.The
The Droste Effect, named after the image on boxes of Droste cocoa powder, refers to an image that contains within it a smaller version of the image, which in turn contains an even smaller version,
Problems 75–84. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
Show thatLet 1+ 2+ + (n − 1) + n = ... n(n+1) 2
Problems 75–84. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
If the terms of a sequence have the property thatLet r equal the common ratio so a₁ az || a2 az an-1, show that an n a2 a1 an+1
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
Problems 75–84. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If
Problems 75–84. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 75–84. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Christine contributes $100 each month to her 401(k). What will be the value of Christine’s 401(k) after the 360th deposit (30 years) if the per annum rate of return is assumed to be 8% compounded
Esmeralda wants to purchase a new home. Suppose that she invests $400 per month into a mutual fund. If the per annum rate of return of the mutual fund is assumed to be 6% compounded monthly, how much
Malik contributes $1000 to an individual retirement account (IRA) semiannually. What will the value of the IRA be when Malik makes his 30th deposit (after 15 years) if the per annum rate of return is
For a child born in 2022, the cost of a 4-year college education at a public university is projected to be $185,000. Assuming a 4.75% per annum rate of return compounded monthly, how much must be
Suppose x, y, and z are consecutive terms in a geometric sequence. If x + y + z = 103 and x2 + y2 + z2 = 6901, find the value of y. Let r be the common ratio so y = xr and z = yr = xr2.
The area inside the fractal known as the Koch snowflake can be described as the sum of the areas of infinitely many equilateral triangles, as pictured below. For all but the center (largest)
Problems 105 – 113. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 105 – 113. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 105 – 113. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
You are interviewing for a job and receive two offers for a five-year contract:A: $40,000 to start, with guaranteed annual increases of 6% for the first 5 yearsB: $44,000 to start, with guaranteed
Problems 105 – 113. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 105 – 113. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 105 – 113. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 105 – 113. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as

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