CALCULUS:GRAPHICAL,NUMERICAL,..-PACKAGE
5th Edition
ISBN: 9780133320381
Author: Finney
Publisher: SAVVAS L
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Suppose f(x)=x^4+3x+1 on the interval [−4,−1].
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- If xis large, which function grows faster, f(x)=2x or g(x)=x2?arrow_forwardFind the linearization L(x) of the function at a. f(x) = x^4/5, a = 32 its not 45, its 4 over 5 like the fractionarrow_forward1. Sketch f(x) = x^3-5.00x^2+1.01x+1.88, showing the roots near+-1 and 5. Write: x = g(x) = (5.00x^2-1.01x-1.88) (x^2) Find the root starting from x0 = 5,4,1,-1. Explain the results. Find a form x = g(x) of f(x) = 0 in problem 1 that yields convergence to the root near x=1.arrow_forward
- (part 1 of 4) Find the nth-derivative, f(n), of f(x) e2x+4. 1. f(n)(x) 2. f(n)(x) 4. f(n) (x) 5. f(n) (x) 1. T3(x) 3. f(n)(x) = — - ²x- n! e²x+4 2. T3(x) 3. T3(x) - = 6. T3(x) = = = = 6. f(n)(x) = n! e²x+4 = (part 2 of 4) Find the degree three Taylor polynomial T3 centered at x = 0 for f when f(x) In(3 – 4x). 2n2x+4 n! = n! 2ne2x+4 2ne²x+4 4 = In 3- col e²x+4 3x 5. T3(x) In 3 4 4. T3(x) = x ₁ -x + T 4 -X 3 8 4 In 3+x 3 9 8 4 =x + 3 4 8 3⁰⁰ ∞ 18 + =x² + 8 9 64 81 8 2 64 8 81 -x3 n3 64 81 3 64 81 23 32 81 تر 64 81arrow_forward9) Choose the correct inverse for the linear functions. f(x) = -4x - 1 O g(2) = O g(z) = O de) -- g(x) : %3D 4 O g(x) = x+4 this work is prohibited without express V ©2015, Responsive Education Solutions. All rights reserved. Reproduction of all or portions from Responsive Education Solutions. 112 3.arrow_forwardSolve (g). Find the derivative of f.arrow_forward
- In Exercises 1-4, find the first derivative of the function. 1. f(x) = V4 –x 2. f(x) = V9 - x?arrow_forwardIn Exercises 21-24, sketch the graph of a function f that has the listed characteristics. 21. f(1) = 2, f'(1) = 0, f'(3) = 2 22. f'(-3) = 0, f'(-1) = 0, f'(2) = 0 23. f(-1) = 2, f'(-1) = 3, ƒ(1) = -2, f'(1) = 3 24. f'(-2) = 2, f'(0) = 1, f(1) = –5arrow_forward6arrow_forward
- Example 1Start with the basic function. f(x)=2x. If you have an initial value of 1, then youend up with the following iterations.• f (1)= 2 • 1= 2 f^2 (1)= 2• 2• 1=4 f^3 (1)= 2• 2• 2• 1=8 A). If you continue this pattern, what do you expect would happen to thenumbers as the number of iterations grows? Check your result by conducting at least 10 iterations. B) Repeat the process with an initial value of −1. What happens as the number of iterations grows?arrow_forwardIn Exercises 22–27, find a formula for the derivative of the function using the difference quotient. 22. g(x)= 2x² – 3 23. m(x) = 1/(x + 1)arrow_forwardFind f^-1 for the function f(x) 3 cubed root x-2 +8arrow_forward
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