Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Student Edition + Mathxl 1-year License
5th Edition
ISBN: 9780133314533
Author: Prentice Hall
Publisher: Prentice Hall
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Describe the end behavior of each function.
7) f(x) = x- 2x' +x-1
8) f(x)=-x² + 8x - 17
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F(t) = e^2t - 8/ 1-t
Will this be undefined? And why? And which values of t is the function
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- If xis large, which function grows faster, f(x)=2x or g(x)=x2?arrow_forward6arrow_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_forward
- In Exercises 1-4, find the first derivative of the function. 1. f(x) = V4 –x 2. f(x) = V9 - x?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_forwardSuppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.arrow_forward
- Describe the sequence of transformations from the related common function f(x)=x' to g. g(x)= 2(x- 8)³arrow_forwardIf sales N(x) are expressed as a function of the amount a spent on advertising, then the dollar amount at which N' (x), the rate of change of sales, goes from increasing to decreasing is call the [Select] If d is that dollar amount, then (d, N(d)) is [Select] ✓ of N(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_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_forwardSolve (g). Find the derivative of f.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_forward
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