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mathematics
precalculus

Questions and Answers of Precalculus

In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun: a1 = 0.4, an = 0.4 + 0.3•2n-2, n ≥ 2where n
Approximating f(x) = ex Refer to problem 89.(a) Approximate with f(- 2.4) with n = 3.(b) Approximate f(-2,5) with n = 6.(c) Use a calculator to approximate f( -2,4).(d) Using trial and error
Approximating f(x) = ex In calculus, it can be shown thatWe can approximate the value of f(x) = ex for any x using the following sumfor some n.(a) Approximate f(1.3) with n = 4.(b)
Use the result of Problem 86 to do the following problems: (a) Write the first 11 terms of the Fibonacci sequence. (b) Write the first 10 terms of the ratio un + 1/ un.(c) As n gets large,
Divide the triangular array shown (called Pascal’s triangle) using diagonal lines as indicated. Find the sum of the numbers in each diagonal row. Do you recognize this sequence? 4 10 10 6. 15
Let,define the nth term of a sequence. (a) Show that u1 = 1 and u2 = 1.(b) show that un + 2 = un + 1 + un.(c) Draw the conclusion that {un} is a Fibonacci sequence. (1 + V5)" – (1 – V5)- 2"
A colony of rabbits begins with one pair of mature rabbits, which will produce a pair of offspring (one male, one female) each month. Assume that all rabbits mature in 1 month and produce a pair of
The Environmental Protection Agency (EPA) determines that Maple Lake has 250 tons of pollutant as a result of industrial waste and that 10% of the pollutant present is neutralized by solar oxidation
Phil bought a car by taking out a loan for $18,500 at 0.5% interest per month. Phil’s normal monthly payment is $434.47 per month, but he decides that he can afford to pay $100 extra toward the
A pond currently has 2000 trout in it. A fish hatchery decides to add an additional 20 trout each month. In addition, it is known that the trout population is growing 3% per month. The size of the
John has a balance of $3000 on his Discover card that charges 1% interest per month on any unpaid balance. John can afford to pay $100 toward the balance each month. His balance each month after
Find the sum of the sequence. 24 Σ3 k=4
Find the sum of the sequence. 20 .3 k=5
Find the sum of the sequence. 40 Σ(-3k) k=8
Find the sum of the sequence. 60 Σ (2k) k=10
Find the sum of the sequence. 14 Σ(2-4) k=0
Find the sum of the sequence. 16 Σ(+4 ) k=1
Find the sum of the sequence. 26 Σ (3k-7) k=1
Find the sum of the sequence. 20 2 (5k + 3) k=1
Find the sum of the sequence. 24 Σ(-k) k=1
Find the sum of the sequence. 40 Σk k=1
Find the sum of the sequence. 50 Σε k=1
Find the sum of the sequence. 40 Σ5 k=1
Express the sum using summation notation. a + ar + ar2 + … arn-1
Express the sum using summation notation. a + (a + d) + (a + 2d) + … + (a + nd)
Express the sum using summation notation.
Express the sum using summation notation. 32. 33 3 + 2 3т п 3.
Express the sum using summation notation. 11 2. 12 9. 27 2/3
Express the sum using summation notation. + (-1)° 36 3 27
Express the sum using summation notation. 1 + 3 + 5 + 7 + ... + [2(12) - 1]
Express the sum using summation notation. 3 13 + ... + 4 13 + 1 3
Express the sum using summation notation. 13 + 23 + 33 + … + 83
Express the sum using summation notation. 1 + 2 + 3 + ... + 20
Write out the sum. п Σ-1)12* k=3
Write out the sum. п Σ-1 Iη k k=2
Write out the sum. n-1 E (2k + 1) k=0
Write out the sum. п-1 Σ 3k+1 k=0
Write out the sum. п 3 (2, k=0
Write out the sum. п k=0 3k
Write out the sum. п Σ (k+ 1)? k=1
Write out the sum. k2 п k=1
Write out the sum. п У (2k + 1) k=1
Write out the sum. п Σ (& + 2) k=1
A sequence is defined recursively. Write down the first five terms. an-1 V2: an 2
A sequence is defined recursively. Write down the first five terms. У2; а, V2 + an-1 a1 = An
A sequence is defined recursively. Write down the first five terms.a1 = A, an = ran-1 , r ≠ 0
A sequence is defined recursively. Write down the first five terms.a1 = A, an = an-1 + d
A sequence is defined recursively. Write down the first five terms.a1 = -1, a2 = 1, an = an-2 + nan-1
A sequence is defined recursively. Write down the first five terms.a1 = 1, a2 = 2, an = an-1. an-2
A sequence is defined recursively. Write down the first five terms.a1 = -2, an = n + 3an - 1
A sequence is defined recursively. Write down the first five terms.a1 = 3, an = an – 1/n
A sequence is defined recursively. Write down the first five terms.a1 = 2, an = -an - 1
A sequence is defined recursively. Write down the first five terms.a1 = 5, an = 2an - 1
A sequence is defined recursively. Write down the first five terms.a1 = 1, an = n – an-1
A sequence is defined recursively. Write down the first five terms.a1 = -2, an = n + an-1
A sequence is defined recursively. Write down the first five terms.a1 = 3, an = 4 – an-1
A sequence is defined recursively. Write down the first five terms.a1 = 2; an = 3 + an-1
The given pattern continues. Write down the nth term of a sequence {an} suggested by the pattern.2, -4, 6, -8, 10....
The given pattern continues. Write down the nth term of a sequence {an} suggested by the pattern.1, -2, 3, -4, 5, -6,...
The given pattern continues. Write down the nth term of a sequence {an} suggested by the pattern. 3, 1, 7, 1. 5, 6'
The given pattern continues. Write down the nth term of a sequence {an} suggested by the pattern.1, -1, 1 -1, 1, -1 ....
The given pattern continues. Write down the nth term of a sequence {an} suggested by the pattern. 2 4 8 16 3'9' 27' 81
The given pattern continues. Write down the nth term of a sequence {an} suggested by the pattern. 1 1 1 2'4'8
The given pattern continues. Write down the nth term of a sequence {an} suggested by the pattern. 1 1 1 1 1.2' 2.3'3.4' 4.5'
The given pattern continues. Write down the nth term of a sequence {an} suggested by the pattern. 1 2 3 4 2'3'4' 5'
Write down the first five terms of the sequence.
Write down the first five terms of the sequence. п {b„} en
Write down the first five terms of the sequence.
Write down the first five terms of the sequence.
Write down the first five terms of the sequence. {()'} {s„} (3,
Write down the first five terms of the sequence. 2" {s„} 3" + 1
Write down the first five terms of the sequence. (d.,) = {(-1)-(,")} {"p} 2n – 1
Write down the first five terms of the sequence. {Cn} = {(-1)n+1 n2}
Write down the first five terms of the sequence. 2n + 1 {b,} 2n
Write down the first five terms of the sequence. п {a,} п+2,
Write down the first five terms of the sequence. {Sn} = {n2 + 1}
Write down the first five terms of the sequence. {Sn} = {n}
Evaluate the factorial expression.5!8!/3!
Evaluate the factorial expression.3!7!/4!
Evaluate the factorial expression.12!/10!
Evaluate the factorial expression.9!/10!
Evaluate the factorial expression.9!
Evaluate the factorial expression.10!
True or False. n(n + 1) +п- п Ek = 1 + 2 + 3 + ·. k=1
The notation is an example of________notation. п Σα + an а1 + аz + aз + . k=1 ||
The sequence a1 5, an 3an-1 is an example of a _____ sequence.
If n ≥ 0 is an integer, then n! = _______ when n ≥ 2.
True or False.The notation a5 represents the fifth term of a sequence.
A(n) is a__________function whose domain is the set of positive integers
True or False.A function is a relation between two sets D and R so that each element x in the first set D is related to exactly one element y in the second set R.
For the function f(x) = x -1/x, find f(2) and f(3).
f(x) = x3 – 3x + 5(a) Using a graphing utility, graph and approximate the zero(s) of f.(b) Using a graphing utility, approximate the local maxima and local minima. (c) Determine the intervals
Graph each equation. (a) y = 3x + 6 (b) x2 + y2 = 4(c) y = x3(d) y = 1/x(e) y = √x(f) y = ex(g) y = lnx (h) 2x2 + 5y2 = 1(i) x2 – 3y2 = 1(j) x2 – 2x – 4y + 1 = 0
The function f(x) = 5/x+2 is one to one. Find f-1 .Find the domain and the range of f and the domain and the range of f-1
Graph f(x) = 3x-2 + 1 using transformations. What is the domain, range, and horizontal asymptote of f?
Find the center and radius of the circle x2 + y2 – 2x + 4y – 11 = 0. Graph the circle.
Determine whether the function is even, odd, or neither. Is the graph of symmetric with respect to the x-axis, y-axis, or origin? 2x3 g(x) : x* + 1
Solve the equation. 3x = e
Solve the equation. log3(x – 1) + log3(2x + 1) = 2
Solve the equation. 3x = 9x+1

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