(a) Find the
(b) Find the
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- For the following exercises, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval. f(x)=2x3x, between x=1 and x=1.arrow_forwardConsider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6 w(x)=x+3x3+6x+9x (a) Which of these rational functions has a horizontal asymptote? (b) Which of these functions has a slant asymptote? (c) Which Of these functions has no vertical asymptote? (d) Which Of these functions has a "hole"? (e) What are the asymptotes of the function r(x) ? (f) Graph y =u(x) , showing clearly any asymptote and x- and y intercepts the function may have. (g) Use long division to find a polynomial P that has the same end behavior as t. graph both P and t on the same screen to verify that they have the sane end behavior.arrow_forwardWhich of the following statements couldn't possibly be true about the polynomial function P? (a) P has degree 3, two local maxima, and two local minima. (b) P has degree 3 and no local maxima or minima. (c) P has degree 4, one local maximum, and no local minima.arrow_forward
- Determine the third Taylor polynomial of the function at x = a. f(x) = x 2 + x + 1, a = 4 O 21 + 9(x - 4) + 9(x - 4)² + 21(x - 4)³ O 5+ 9(x - 4) + 13(x - 4)2 O 21 + 9(x - 4) + (x - 4)2 O 1+ 3(x - 4)+ 3(x - 4)2 + (x - 4)3 A Moving to the next question prevents changes to this answer. e Type here to search PrtScn DII F3 F7 F5 F6 F4arrow_forwardFind the third degree Taylor polynomial centered at c = 1 for the function. f(x) = √x Select one: O a. O b. O d. 3 ○ c. 1+ — (x+1)- 32 (x−1)² + O e 7 1 + - 1/² ( x + 1) + 3/2² (x − 1)² - 128 e. 3 1+ (x-1)+(x-1²- / - 32 1+ 1+ (x-1)-3(x-1)² + 32 -(x + 1)³ 7 128 7 128 7 128 -(x - 1)³ (x + 1)³ (x-1)³ 10-1-0-1²-17 (x-1)² - (x− 1)- 3/2 (x - 1)² - 128arrow_forwardLet f(x) = , find L, (x) of the second Lagrange interpolating polynomial, if x, =2, x, =2.5, X2 =4 Select one: a. (x - 6.5)x + 10, b. (0.05x - 0.425)x + 1.15 (-4x + 24)x – 32 3 (x – 4.5)x + 5 O d. 3arrow_forward
- Find the Maclaurin polynomial of degree two for the function f(x) = sec (9x). Select one: O a. O b. O c. ○ d. O O e. 81 P₂(x) = 1 + $12² x ²2 P₂(x)=x- P₂(x) = 1+ 81 81 81 P₂(x) = 1-5/1²x²2 81 P₂(x) = x + ² x ² 2arrow_forward1. The zeros of the polynomial function f (x)=x' – 2x² – 15x are: a. {-5,–3,0} . b. {-3,5} . c. {-5,3} . d. {-5,0,3} . e. {-3,0,5} .arrow_forwardDefine f(n)= II (1 = II ( ¹ - ² ) = (¹ - ²¹ ) · ( ¹ − 3 ) · (¹ – ↓ ) --- (¹ - -/-), - 32 1=2 where n € Z+ and n > 2. Here, Z+ is the set of all positive integers. Find a rational polynomial that is equal to f(n). n ƒ(n) = II (¹-²1) i=2 = Justify this equality by induction. (1)arrow_forward
- Let T(x) denote the Chebyshev polynomial of degree k. Express the composite polynomial Tn(Tm(x)) of degree n · m in terms of Chebyshev polynomials.arrow_forwardFind the Taylor polynomial T3 for the function f(x) = ln(x) at the number a = 1 OA. (x-1)+¹(x - 1)² + OB. (x-1) + (x − 1)² + C. none of these OD. (x + 1)(x + 1)² + OE. (x - 1) — (x − 1)² + (x - 1)³ (x- 1)³ (x + 1)³ (x − 1)³arrow_forwardDetermine whether the following polynomials are even, odd, or neither. (A) f (x) = 5' - 2a- 4x + 1 (B) f (x) = -9a1 - 2x' + 5x + 6x (C) f(x) = -8r°-7x-3r² - 6 7x-3x2arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell