Concept explainers
Miscellaneous limits Use the method of your choice to evaluate the following limits.
67.
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Calculus: Early Transcendentals (2nd Edition)
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Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th Edition)
Precalculus (10th Edition)
Glencoe Math Accelerated, Student Edition
Precalculus Enhanced with Graphing Utilities (7th Edition)
- When you borrow money to buy a house, a car, or for some other purpose, you repay the loan by making periodic payments over a certain period of time. Of course, the lending company will charge interest on the loan. Every periodic payment consists of the interest on the loan and the payment toward the principal amount. To be specific, suppose that you borrow $1,000 at an interest rate of 7.2% per year and the payments are monthly. Suppose that your monthly payment is $25. Now, the interest is 7.2% per year and the payments are monthly, so the interest rate per month is 7.2/12 = 0.6%. The first months interest on $1,000 is 1000 0.006 = 6. Because the payment is $25 and the interest for the first month is $6, the payment toward the principal amount is 25 6 = 19. This means after making the first payment, the loan amount is 1,000 19 = 981. For the second payment, the interest is calculated on $981. So the interest for the second month is 981 0.006 = 5.886, that is, approximately $5.89. This implies that the payment toward the principal is 25 5.89 = 19.11 and the remaining balance after the second payment is 981 19.11 = 961.89. This process is repeated until the loan is paid. Write a program that accepts as input the loan amount, the interest rate per year, and the monthly payment. (Enter the interest rate as a percentage. For example, if the interest rate is 7.2% per year, then enter 7.2.) The program then outputs the number of months it would take to repay the loan. (Note that if the monthly payment is less than the first months interest, then after each payment, the loan amount will increase. In this case, the program must warn the borrower that the monthly payment is too low, and with this monthly payment, the loan amount could not be repaid.)arrow_forwardHeat capacity of a solid: Debye's theory of solids gives the heat capacity of a solid at temperature T to be 3 T rOp/T Cy = 9VpkB (e* – 1)2 dx, - where V is the volume of the solid, p is the number density of atoms, kg is Boltzmann's constant, and 0D is the so-called Debye temperature, a property of solids that depends on their density and speed of sound. Develop a computer code to evaluate Cy (T) for a given value of the temperature, for a sample consisting of 1000 cubic centimeters of solid aluminum, which has a number density of p = 6.022 x 1028m-3 and a Debye temperature of 0p = 428K. The Boltzmann's constant kg = 1.380649 x 10-23 J · K-1. Please evaluate the integral with the following methods: (a) MATLAB adaptive Simpson quadrature, [Q.FCNT] = QUAD(FUN,A,B,TOL) with TOL =le-10.arrow_forwardThe quadratic formula is used to solve a very specific type of equation, called aquadratic equation. These equations are usually written in the following form:ax2 + bx + c = 0The Quadratic Formula x = ( -b ± √( b^2 - 4ac ) ) / ( 2a ) Where a, b, and c are constants with a ≠ 0. (If a = 0, the equation is a linear equation.)The discriminant is the part of the formula in the square root. If the value of the discriminant is zero then the equation has a single real root. If the value of thediscriminant is positive then the equation has two real roots. If the value of thediscriminant is negative, then the equation has two complex roots.Write a program that finds the roots of the quadratic equation using the Quadratic Formula. Write a function named discriminant in the file, Disc.py, to calculate and return the discriminant of the formula. Let the main function call the discriminant function and then calculate the solution(s) of the equation. Do not calculate the solutions in the discriminant…arrow_forward
- Question 5 Numerical Approximation Methods basic ideas: Please write the basic idea (with key equations), application example, advantages and limitations of the following numerical approximation methods for solving linear/nonlinear equations. Please also state cases/examples for which one method can provide good result, but other may not. 1) Relaxation method 2) Binary search method 3) Newton's method 4) Secant method [Note: You can use simple examples for showing their applications. You might not need to derive any method]arrow_forwardJava function to Find whether a given number is a power of 4 or not Example : powerOfFourOrNot(2) -> false powerOfFourOrNot(16) -> truearrow_forwardB=(1)/(4)e*p slove for earrow_forward
- i need solution very very quickly please #data structure in c++# #the question below# The cafeteria in a university decided to make Black Friday, each student can take at most 3items from the cafeteria, if the student has an average greater than or equal 90, he can take all his itemsfor free and if the average between 60 and 89 the student can take 1 item only as free from his items,otherwise the student should pay for the items. before the cafeteria opens the door there are many andmany students waiting at the door, the guard decide to order the students about their averages in a priorityqueue. So the heist average comes first in the queue.Notes:- The student object consists of ID, Name, average and number of buying items between (0,3) items- The number of the students should be created randomly and must be less than 100 students- The number of buying items and the student average are created randomly.- The cafeteria has random number of items less than 200- The price of each item in…arrow_forwardProblem-1: Check if an integer is Prime An integer greater than 1 is prime if its only positive divisor is 1 or itself. For example, 2, 3, 5, and 7 are prime numbers, but 4, 6, 8, and 9 are not. Key idea: To test whether a number is prime, check whether it is divisible by 2, 3, 4, and so on up to number/2. If a divisor is found, the number is not a prime. The algorithm can be described as follows: Use a boolean variable isPrime to denote whether the number is prime; Set isPrime to true initially; for (int divisor = 2; divisor <= number / 2; divisor++) { if (number % divisor == 0) { Set isPrime to false Exit the loop; } }arrow_forwardCalculate the following if a =[1, -3,5] & b =[4,0,8] 2. a x b 1. a∙barrow_forward
- (Data processing) Your professor has asked you to write a C++ program that determines grades at the end of the semester. For each student, identified by an integer number between 1 and 60, four exam grades must be kept, and two final grade averages must be computed. The first grade average is simply the average of all four grades. The second grade average is computed by weighting the four grades as follows: The first grade gets a weight of 0.2, the second grade gets a weight of 0.3, the third grade gets a weight of 0.3, and the fourth grade gets a weight of 0.2. That is, the final grade is computed as follows: 0.2grade1+0.3grade2+0.3grade3+0.2grade4 Using this information, construct a 60-by-7 two-dimensional array, in which the first column is used for the student number, the next four columns for the grades, and the last two columns for the computed final grades. The program’s output should be a display of the data in the completed array. For testing purposes, the professor has provided the following data:arrow_forwardComplete the following codearrow_forwardposting multiple times answer only 100% knowledge else skiparrow_forward
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage LearningC++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr