Determine if the following statements are true or false. TRUE or FALSE, and you must briefly justify your answer you must clearly state a. If f (x) = 2 cos x then , f(x) = 2 f(x) for any real number a. %3D b. If r(x) is a rational function and a is any real number, then lim r(x) = r(a) X→a C. If a function h(x) is continuous, h' (x) < 0, and h"(x) > 0 for all x in (-o, o0), then h(x) must be positive for some value of x.

Determine if the following statements are true or false. TRUE or FALSE, and you must briefly justify your answer you must clearly state a. If f (x) = 2 cos x then , f(x) = 2 f(x) for any real number a. %3D b. If r(x) is a rational function and a is any real number, then lim r(x) = r(a) X→a C. If a function h(x) is continuous, h' (x) < 0, and h"(x) > 0 for all x in (-o, o0), then h(x) must be positive for some value of x.

Name: I need help this is a nongraded question. Determine if the following s
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Description: I need help this is a nongraded question. Determine if the following statements are true or false.TRUE or FALSE, and you must briefly justify your answer!you must clearly statea. If f(x) = 2 cos x then f(x) = 2 - f(x) for any real number a.b. If r(x)

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section: Chapter Questions

Problem 11T: Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6...

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Consider 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.
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a) Find the values of α and β such that the functionf(x) = (α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0 if x ≥ 0 is continuous on the interval (−∞,∞).(b) For which values of α and β is the function f(x) differentiable?