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mathematics
calculus with applications
Calculus With Applications 12th Edition Margaret L. Lial - Solutions
Use Taylor polynomials of degree 4 at x = 0, found in Exercises above, to approximate the quantities in Exercises. Round to 4 decimal places.4.023/2
Use Taylor polynomials of degree 4 at x = 0, found in Exercises above, to approximate the quantities in Exercises. Round answers to 4 decimal places. 1.06
Find the payments necessary to amortize each loan.$41,000, 12% compounded semiannually, 10 semiannual payments
Use Newton’s method to find the critical points for the functions defined as follows. Approximate them to the nearest hundredth. Decide whether each critical point leads to a relative maximum or a relative minimum.ƒ(x) = x3 + 9x2 - 6x + 4
Use l’Hospital’s rule where applicable to find each limit. lim x 1 Vx2 +5x + 9 x - 1
Identify the geometric series that converge. Give the sum of each convergent series.9 - 6 + 4 - 8/3 +...
Find the sum of the first five terms of each geometric sequence.a1 = 6.324, r = 2.598
Find the payments necessary to amortize each loan.$55,000, 6% compounded monthly, 36 monthly payments
Use Newton’s method to find the critical points for the functions defined as follows. Approximate them to the nearest hundredth. Decide whether each critical point leads to a relative maximum or a relative minimum.ƒ(x) = x4 - 3x3 + 6x - 1
Mitzi drops a ball from a height of 10 m and notices that on each bounce the ball returns to about 3/4 of its previous height. About how far will the ball travel before it comes to rest?
Use the method in Example 4 (with five terms of the appropriate Taylor series) to approximate the areas of the following regions.The region bounded by ƒ(x) = 1/(1 - √x), x = 1/4, x = 1/3, and the x-axisExample 4The standard normal curve of statistics is given byFind the area bounded by this
Identify the geometric series that converge. Give the sum of each convergent series.2 + 1.4 + 0.98 + 0.686 +...
Use l’Hospital’s rule where applicable to find each limit. lim x-0 (5 + x)ln(x + 1) et - 1
Find the sum of the first five terms of each geometric sequence.a1 = -2.772, r = -1.335
Find the payments necessary to amortize each loan.$6800, 12% compounded monthly, 24 monthly payments
Use Newton’s method to find the critical points for the functions defined as follows. Approximate them to the nearest hundredth. Decide whether each critical point leads to a relative maximum or a relative minimum.ƒ(x) = x4 + 2x3 - 5x + 2
Use the formula for the sum of the first n terms of a geometric sequence to evaluate the following sums. 7 Σ8(2) =0
Use Newton’s method to attempt to find a solution for the equation ƒ(x) = (x - 1)1/3 = 0 by starting with a value very close to 1, which is obviously the true solution. Verify that the approximations get worse with each iteration of Newton’s method. This is one of those rare cases in which
After a person pedaling a bicycle removes his or her feet from the pedals, the wheel rotates 400 times the first minute. As it continues to slow down, in each minute it rotates only 3/4 as many times as in the previous minute. How many times will the wheel rotate before coming to a complete stop?
Use the method in Example 4 (with five terms of the appropriate Taylor series) to approximate the areas of the following regions.The region bounded by ƒ(x) = e√x, x = 0, x = 1, and the x-axisExample 4The standard normal curve of statistics is given byFind the area bounded by this curve and the
Use Taylor polynomials of degree 4 at x = 0, found in Exercises above, to approximate the quantities in Exercises. Round answers to 4 decimal places.1n 0.97
Use l’Hospital’s rule where applicable to find each limit. lim x-0 (7x)In(1-x) ex 1 -
Identify the geometric series that converge. Give the sum of each convergent series.3 + 9 + 27 + 81 +...
Sarah wants to deposit $12,000 at the end of each year for 9 years into an annuity.(a) Sarah’s local bank offers an account paying 5% interest compounded annually. Find the final amount she will have on deposit.(b) Sarah’s brother-in-law works in a bank that pays 3% compounded annually. If she
For a particular product, the revenue and cost functions are R(x) = 10x2/3 and C(x) = 2x - 9 Approximate the break-even point to the nearest hundredth.
Use the formula for the sum of the first n terms of a geometric sequence to evaluate the following sums. 6 Σ4(3) i=0
A pendulum bob swings through an arc 40 cm long on its first swing. Each swing thereafter, it swings only 80% as far as on the previous swing. How far will it swing altogether before coming to a complete stop?
Use l’Hospital’s rule where applicable to find each limit. lim_x²(In x)² x-0
Use Taylor polynomials of degree 4 at x = 0, found in Exercises above, to approximate the quantities in Exercises. Round answers to 4 decimal places.1n 1.06
Identify the geometric series that converge. Give the sum of each convergent series.4 + 4.8 + 5.76 + 6.912 +...
Use the formula for the sum of the first n terms of a geometric sequence to evaluate the following sums. IM ∞
For 8 years, Yvette deposits $100 at the end of each month into an annuity paying 6% annual interest compounded monthly.(a) Find the total amount Yvette deposits into the account over the 8 years.(b) Find the final amount Yvette will have on deposit at the end of the 8 years.(c) How much interest
As mentioned in Example 4, the equation of the standard normal curve isUse the method in Example 4 (with five terms of the Taylor series) to approximate the area of the region bounded by the normal curve, the x-axis, x = 0, and the values of x in Exercises.x = 0.4Example 4The standard normal curve
A new manufacturing process produces savings of S(x) = x2 + 40x + 20 dollars after x years, with increased costs of C(x) = x3 + 5x2 + 9 dollars. For how many years, to the nearest hundredth, should the process be used?
Federal government regulations require that people loaning money to consumers disclose the true annual interest rate of the loan. The formulas for calculating this interest rate are very complex. For example, suppose P dollars is loaned, with the money to be repaid in n monthly payments of M
Identify the geometric series that converge. Give the sum of each convergent series. 2 5 | 2 25 + 2 125 2 625 +
A sequence of equilateral triangles is constructed as follows: The first triangle has sides 2 m in length. To get the next triangle, midpoints of the sides of the previous triangle are connected. If this process could be continued indefinitely, what would be the total perimeter of all the triangles?
Use Taylor polynomials of degree 4 at x = 0, found in Exercises above, to approximate the quantities in Exercises. Round answers to 4 decimal places.1n 1.008
Use l’Hospital’s rule where applicable to find each limit. lim xel/x x-0
Isaac wants $20,000 in 8 years.(a) What amount should he deposit at the end of each quarter at 6% annual interest compounded quarterly to accumulate the $20,000?(b) Find his quarterly deposit if the money is deposited at 4% compounded quarterly.
As mentioned in Example 4, the equation of the standard normal curve isUse the method in Example 4 (with five terms of the Taylor series) to approximate the area of the region bounded by the normal curve, the x-axis, x = 0, and the values of x in Exercises.x = 0.6Example 4The standard normal curve
What would be the total area of all the triangles of Exercise 37, disregarding the overlaps?Exercise 37A sequence of equilateral triangles is constructed as follows: The first triangle has sides 2 m in length. To get the next triangle, midpoints of the sides of the previous triangle are connected.
Use Taylor polynomials of degree 4 at x = 0, found in Exercises above, to approximate the quantities in Exercises. Round answers to 4 decimal places.1n 0.992
Find a4 and an for the following geometric sequences. Then find the sum of the first five terms.a1 = 5, r = -2
Find a5 and an for the following geometric sequences.a1 = -3, r = -5
Find the amount of each ordinary annuity based on the information given.R = $1800, 8% interest compounded quarterly for 12 years
Use l’Hospital’s rule where applicable to find each limit. -x xe lim x-0 2e²x - 2
In Exercises, find the Taylor series for the functions defined as follows. Give the interval of convergence for each series. f(x) 9x4 1 - x
For the functions defined as follows, find the Taylor polynomials of degree 4 at 0. f(x) = √x + 16 Vx
Identify which geometric series converge. Give the sum of each convergent series. 4 5 + 25 + 5 +
Identify which geometric series converge. Give the sum of each convergent series. 1 3 2 9 4 + 27 I 8 81 +
Use Newton’s method to find a solution for each equation in the given intervals. Find all solutions to the nearest hundredth.4x1/3 - 2x2 + 4 = 0; [-3, 0]
Use l’Hospital’s rule where applicable to find each limit. lim et x→0 2x³ + 9x² - 11x
Find a4 and an for the following geometric sequences. Then find the sum of the first five terms.a1 = 128, r = 1/2
Find a5 and an for the following geometric sequences.a1 = -4, r = -2
Find the amount of each ordinary annuity based on the information given.R = $5300, 4% interest compounded quarterly for 9 years
Use Newton’s method to find a solution for each equation in the given intervals. Find all solutions to the nearest hundredth.4x1/3 - 2x2 + 4 = 0; [0, 3]
Identify which geometric series converge. Give the sum of each convergent series. 1 + 1 1.01 + 1 (1.01)²
Use l’Hospital’s rule where applicable to find each limit. lim x→0 8x5 et 3x4
In Exercises, find the Taylor series for the functions defined as follows. Give the interval of convergence for each series. f(x) = In 1 : In (1 X 2,
In Exercises, find the Taylor series for the functions defined as follows. Give the interval of convergence for each series.ƒ(x) = ln(1 + 4x)
For the functions defined as follows, find the Taylor polynomials of degree 4 at 0.ƒ(x) = ln(1 - x)
Find a4 and an for the following geometric sequences. Then find the sum of the first five terms.a1 = 27, r = 1/3
Find a5 and an for the following geometric sequences.a2 = 12, r = 1/2
Find the periodic payments that will amount to the given sums under the given conditions.S = $10,000; interest is 8% compounded annually; payments are made at the end of each year for 12 years.
Use Newton’s method to find a solution for each equation in the given intervals. Find all solutions to the nearest hundredth.ex + x - 2 = 0; [0, 3]
Identify which geometric series converge. Give the sum of each convergent series. e-1+ e 1 헐 +
Use l’Hospital’s rule where applicable to find each limit. lim x-0 √2+x-√2 X
Find the periodic payments that will amount to the given sums under the given conditions.S = $80,000; interest is 6% compounded semiannually; payments are made at the end of each semiannual period for 9 years.
Find a5 and an for the following geometric sequences.a3 = 2, r = 1/3
Use Newton’s method to find a solution for each equation in the given intervals. Find all solutions to the nearest hundredth.e2x + 3x - 4 = 0; [0, 3]
Find a4 and an for the following geometric sequences. Then find the sum of the first five terms.a1 = 2, r = -5
Use l’Hospital’s rule where applicable to find each limit. lim x-0 V9 + x - 3 X
In Exercises, find the Taylor series for the functions defined as follows. Give the interval of convergence for each series.ƒ(x) = e4x2
For the functions defined as follows, find the Taylor polynomials of degree 4 at 0.ƒ(x) = ln(1 + 2x2)
Find Taylor polynomials of degree 4 at 0 for the functions defined as follows.ƒ(x) = e2-x
Find a5 and an for the following geometric sequences.a4 = 64, r = -4
In Exercises, the nth term of a sequence is given. Calculate the first five partial sums. an = 1 2n + 5
Find the periodic payments that will amount to the given sums under the given conditions.S = $50,000; interest is 12% compounded quarterly; payments are made at the end of each quarter for 8 years.
In Exercises, the nth term of a sequence is given. Calculate the first five partial sums. an 1 n
Use Newton’s method to find a solution for each equation in the given intervals. Find all solutions to the nearest hundredth.x2e-x + x2 - 2 = 0; [0, 3]
Identify which geometric series converge. Give the sum of each convergent series.e + e2 + e3 + e4 +...
In Exercises, find the Taylor series for the functions defined as follows. Give the interval of convergence for each series.ƒ(x) = e-3x2
For the functions defined as follows, find the Taylor polynomials of degree 4 at 0.ƒ(x) = ln(1 - x3)
Use l’Hospital’s rule where applicable to find each limit. √x - 2 lim X-4 X - 4
Find Taylor polynomials of degree 4 at 0 for the functions defined as follows.ƒ(x) = 5e2x
Find a5 and an for the following geometric sequences.a4 = 81, r = -3
Find the periodic payments that will amount to the given sums under the given conditions.S = $8000; interest is 4% compounded monthly; payments are made at the end of each month for 5 years.
In Exercises, the nth term of a sequence is given. Calculate the first five partial sums. ап = 1 n+ 1
Use Newton’s method to find a solution for each equation in the given intervals. Find all solutions to the nearest hundredth.x2e-x + x2 - 2 = 0; [-3, 0]
Use l’Hospital’s rule where applicable to find each limit. √x - 3 9 lim x 9 x
In Exercises, find the Taylor series for the functions defined as follows. Give the interval of convergence for each series.ƒ(x) = x3e-x
For the functions defined as follows, find the Taylor polynomials of degree 4 at 0.ƒ(x) = xe-x
Find Taylor polynomials of degree 4 at 0 for the functions defined as follows. f(x) = √x + 27
Find Taylor polynomials of degree 4 at 0 for the functions defined as follows.ƒ(x) = √x + 1
For each sequence that is geometric, find r and an.4, 16, 64, 256,...
Find the present value of each ordinary annuity.Payments of $5000 are made annually for 11 years at 6% compounded annually.
Use Newton’s method to find a solution for each equation in the given intervals. Find all solutions to the nearest hundredth.1n x + x - 2 = 0; [1, 4]
In Exercises, find the Taylor series for the functions defined as follows. Give the interval of convergence for each series.ƒ(x) = x4e2x
For the functions defined as follows, find the Taylor polynomials of degree 4 at 0.ƒ(x) = x2ex
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