wsweis expressed as regular Tractions instead of decimals. Do not use mixed numbers in this class....
1. Find the cubic function that models the data in the table below. x -2,-1,0,1,2,3,4 y 48,9,0,3,0,-27,-96 y= ______? (Simplify your answer. Do not factor. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) 2. Find the quartic function that is the best fit for the data in the table below. Report the model with three significant digits in the coefficients. x -2,-1,0,1,2,3,4 y 1,-0.5,0,-0.5,1,13.5,52 y = ______ ? (Simplify your answer....
3. (5 pts) For each of the listed functions, determine a formula for the derivative function. For the first two, determine the formula for the derivative by thinking about the nature of the given function and its slope at various points; do not use the limit definition. For the latter three, use the limit definition, Pay careful attention to the function names and independent variables. It is important to be comfortable with using letters other than f and r. For...
*PLEASE DO IN MATHEMATICA*
{:1, ifr+ 13. Consider the function f(x)- nction,f(x)-e-r/rifx#0 a. Plot the graph of this function using Mathematica. b. Use the limit definition of the derivative and LHopital's Rule to show that every higher-order derivative of f at r 0 vanishes. c. Find the MacLaurin series for f. Does the series converge to f?
{:1, ifr+ 13. Consider the function f(x)- nction,f(x)-e-r/rifx#0 a. Plot the graph of this function using Mathematica. b. Use the limit definition of...
5x + 1 Use the definition of the derivative to find the derivative of the function f(x) = *-*2. Then find all x-values (if any) where the tangent line is horizontal. If the tangent line is horizontal for all X, write R for your answer. If the tangent line is never horizontal, write None for your answer Answer 3 Points Keypad 11 1'(x) = 2 Tangent is horizontal at x = Prev Nex If f(3) = -1, f(3) = 17,...
In Python 3.6
Classes and Methods: A class for estimating the derivative of a function f) at the form: takes where h is a small change in x. The goal of this exercise is to use the formula above to differentinte a mat hematical function f(x) implemented as a Python function f(x) Implement class Diff with two special methods. The--init--() method takes in function object and also an optional argument h. The default value of h is le-4. Implement also...
Section 2.6 Homework (continued) D. Determine the end behavior of the following function. (Do this algebraically.) $ 16x8 – 12x2 f(x) = 1- 7x² + 5x 70 + 2X-8 C. Find the limit or show that it does not exist. (a.) lim n sin²x " (Hint: Use squeeze theorem) X x²+1 (b.) lim cot?(-Inx) (Do this analytically.) X-> Section 2.6 Homework (continued) E. Find the following limits if they exist. Explain. (Do this analytically (a.) lim cot' (In 10 -...
(3) Use the first derivative test to classify the critical numbers of the function s(x) = r -4.r" +17. That is, identify the location of any local maximums or minimums. (4) Find the equation of the line tangent to f(0) = 127-22 at the point (4,8).
Computer Programming II (CS141) Q.1. Why would you use an inner class instead of regular class? Q.2. What does this code print? Why is it polymorphic? DataSet data = new DataSet(); data.add(new BankAccount(1000)); data.add(new Coin(0.1, "dime")); System.out.println(data.getAverage()); Q.3. Can you convert a superclass reference into a subclass reference? A subclass reference into a superclass reference? If so, give examples. If not, explain why not. Q.4. Implement a superclass Person. Make two classes, Student and Instructor that inherit from Person. A...
A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in...