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For each of the functions below, the floating-point evaluation of the given function is very inaccurate...
1. (a) We need to calculate accurate values of the function for very large values of x. However, it is found that ju...
1. (a) We need to calculate accurate values of the function for very large values of x. However, it is found that just programming this formula into a computer gives very poor accuracy for large x Explain why this happens, and show how to re-write the function so that it can be used reliably, even when x is large. [6 points] (b) In diffraction theory, it is sometimes necessary to evaluate the function sin θ f(x) for small to moderate...
(1 point) Taylor's Remainder Theorem: Consider the function 1 f(x) = The third degree Taylor polynomial...
(1 point) Taylor's Remainder Theorem: Consider the function 1 f(x) = The third degree Taylor polynomial of f(x) centered at a = 2 is given by 1 3 12 60 P3(x) = -(x-2) + -(x - 2)2 – -(x - 2) 23 22! 263! Given that f (4)(x) = how closely does this polynomial approximate f(x) when x = 2.4. That is, if R3(x) = f(x) – P3(x), how large can |R3 (2.4) be? |R3(2.4) 360 x (1 point) Taylor's...
-100x 1. Given the function f(x)=- (1-0.5x) (a) Find the y-intercept point (if there is any):...
-100x 1. Given the function f(x)=- (1-0.5x) (a) Find the y-intercept point (if there is any): (b) Find the x-intercept point(s) (if there is any): (c) Find f'(x): (d) Find critical number(s) of f(x) (Type 1 and Type 2, if there are any): (e) Find the critical point(s) (if there are any): (f) Find the open x-intervals where f(x) increases and decreases: (g) Find the behavior of the function for very large positive x-values (find limit as x goes to...
Create a python add the following functions below to the module. Each section below is a...
Create a python add the following functions below to the module. Each section below is a function that you must implement, make sure the function's names and parameters match the documentation (Copy-Paste). DO NOT put the functions in an if-name-main block. 1. def productSum(x: int, y: int, z: int) -> int This function should return: The product of x and y, if the product of x and y is less than z. Else it should return the sum of x...
In C PLEASE 1.22 LAB: Using math functions Given three floating-point numbers x, y, and z,...
In C PLEASE
1.22 LAB: Using math functions Given three floating-point numbers x, y, and z, output x to the power of z, x to the power of (y to the power of 2), the absolute value of y, and the square root of (xy to the power of z). Output each floating-point value with two digits after the decimal point, which can be achieved as follows: printf("%0.21f", yourValue); Ex: If the input is: 5.0 6.5 3.2 the output is:...
(1 point) Given that a function f(+) has a tangent line at x = 3 given...
(1 point) Given that a function f(+) has a tangent line at x = 3 given by y = 9(2 - 3) + 6. Which of the following could be the Taylor Series representation for f(x)? A 5 n! (x - 3)" 8.5+ ()" (2 – 3)" B n! 9 (-3) D.6+ () (31 - 3)"
dont ans this question Euler's method is based on the fact that the tangent line gives...
dont ans this question
Euler's method is based on the fact that the tangent line gives a good local approximation for the function. But why restrict ourselves to linear approximants when higher degree polynomial approximants are available? For example, we can use the Taylor polynomial of degree about = No, which is defined by P.(x) = y(x) + y (xo)(x – Xa) + 21 (x- This polynomial is the nth partial sum of the Taylor series representation (te) (x –...
(1 point) Find the Maclaurin series and corresponding interval of convergence of the following function. 1...
(1 point) Find the Maclaurin series and corresponding interval of convergence of the following function. 1 f(2) 1+ 72 f(x) = Σ n=0 The interval of convergence is: (1 point) Consider the power series 4)" (x + 2)". Vn n=1 Find the radius of convergence R. If it is infinite, type "infinity" or "inf". Answer: R= What is the interval of convergence? Answer (in interval notation): (1 point) Find all the values of x such that the given series would...
(1 point) Compare and discuss the long-run behaviors of the functions below. In each blank, enter...
(1 point) Compare and discuss the long-run behaviors of the functions below. In each blank, enter either the constant or the polynomial that the rational function behaves like as x + Foo: 23 – 3 1. x4 – 3 f(x) = ar — x2 – 3 23 – 8 , and h(x) = 23 – 8' x3 – 8' f(x) will behave like the function y = as x + +0. help (formulas) g(x) will behave like the function y...
(1 point) Given that a function f(x) has a tangent line at 4 given by y...
(1 point) Given that a function f(x) has a tangent line at 4 given by y = 6(x – 4) +5. Which of the following could be the Taylor Series representation for f(x)? 0 5+ (6)" A. (2 - 4)" n! 10 00 5 B. (2 - 4)" O 4+ (2)" C. ( no n! 4)" 6 D. (2 on! n0 4)"
1. (a) We need to calculate accurate values of the function for very large values of x. However, it is found that just programming this formula into a computer gives very poor accuracy for large x Explain why this happens, and show how to re-write the function so that it can be used reliably, even when x is large. [6 points] (b) In diffraction theory, it is sometimes necessary to evaluate the function sin θ f(x) for small to moderate...
(1 point) Taylor's Remainder Theorem: Consider the function 1 f(x) = The third degree Taylor polynomial of f(x) centered at a = 2 is given by 1 3 12 60 P3(x) = -(x-2) + -(x - 2)2 – -(x - 2) 23 22! 263! Given that f (4)(x) = how closely does this polynomial approximate f(x) when x = 2.4. That is, if R3(x) = f(x) – P3(x), how large can |R3 (2.4) be? |R3(2.4) 360 x (1 point) Taylor's...
-100x 1. Given the function f(x)=- (1-0.5x) (a) Find the y-intercept point (if there is any): (b) Find the x-intercept point(s) (if there is any): (c) Find f'(x): (d) Find critical number(s) of f(x) (Type 1 and Type 2, if there are any): (e) Find the critical point(s) (if there are any): (f) Find the open x-intervals where f(x) increases and decreases: (g) Find the behavior of the function for very large positive x-values (find limit as x goes to...
In C PLEASE
1.22 LAB: Using math functions Given three floating-point numbers x, y, and z, output x to the power of z, x to the power of (y to the power of 2), the absolute value of y, and the square root of (xy to the power of z). Output each floating-point value with two digits after the decimal point, which can be achieved as follows: printf("%0.21f", yourValue); Ex: If the input is: 5.0 6.5 3.2 the output is:...
(1 point) Given that a function f(+) has a tangent line at x = 3 given by y = 9(2 - 3) + 6. Which of the following could be the Taylor Series representation for f(x)? A 5 n! (x - 3)" 8.5+ ()" (2 – 3)" B n! 9 (-3) D.6+ () (31 - 3)"
dont ans this question
Euler's method is based on the fact that the tangent line gives a good local approximation for the function. But why restrict ourselves to linear approximants when higher degree polynomial approximants are available? For example, we can use the Taylor polynomial of degree about = No, which is defined by P.(x) = y(x) + y (xo)(x – Xa) + 21 (x- This polynomial is the nth partial sum of the Taylor series representation (te) (x –...
(1 point) Find the Maclaurin series and corresponding interval of convergence of the following function. 1 f(2) 1+ 72 f(x) = Σ n=0 The interval of convergence is: (1 point) Consider the power series 4)" (x + 2)". Vn n=1 Find the radius of convergence R. If it is infinite, type "infinity" or "inf". Answer: R= What is the interval of convergence? Answer (in interval notation): (1 point) Find all the values of x such that the given series would...
(1 point) Compare and discuss the long-run behaviors of the functions below. In each blank, enter either the constant or the polynomial that the rational function behaves like as x + Foo: 23 – 3 1. x4 – 3 f(x) = ar — x2 – 3 23 – 8 , and h(x) = 23 – 8' x3 – 8' f(x) will behave like the function y = as x + +0. help (formulas) g(x) will behave like the function y...
(1 point) Given that a function f(x) has a tangent line at 4 given by y = 6(x – 4) +5. Which of the following could be the Taylor Series representation for f(x)? 0 5+ (6)" A. (2 - 4)" n! 10 00 5 B. (2 - 4)" O 4+ (2)" C. ( no n! 4)" 6 D. (2 on! n0 4)"
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