(a) By definition, for a function g to be continuous at x = a,lim g(x)Vx – 2(b) Consider f(x)Note that f is not4continuous at x =4.Determine a function g, which agrees with f on it's domainand is continuous at x4.This is an example of removing a discontinuity.Enter answer as reduced fraction.-{- 4g(x) =х — 4

Answered: Image /qna-images/answer/b4eb0ba7-0196-4e12-a431-52ba42265f5d.jpg

Answered: (a) By definition, for a function g to…

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.
S-20 Rational Function Is y=x3+4x2+x+1 is a rational function?
Given the function f(x)= 5+x; x<4; x2-7; X>4 a)On which interval(s) is the function continuous? b)Circle the answer that justifies why the function is continuous on the interval(s) you chose in part (a). A. The function is continuous because f(4) is defined, limx→4 f(x) = f(4). B. The function is continuous because a rational function is continuous at every real number. C. There is a discontinuity at x = 4 because f(4) is not defined and limx→4 f(x) ≠ f(4).
(a) for g(t)= t-9/square root t-3 . Make table of values with at least six appropriate inputs to evaluate the limits as t tends to 9. (b) make a conjecture about the value of lim t-9/square root t-3. t->9
A. Does f(1) exist B. Does lim x->1 f(x) exist C. Does lim x->1 f(x) equal f(1) D. Is the function continuous at x=1
Determine whether f is differentiable at x=0 by considering limh→0f(0+h)−f(0)h. f(x)=18−x Choose the correct answer below. A. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient do not exist at x=0. B. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient exist at x=0, but are not equal. C. The function f is differentiable at x=0 because the graph has a sharp corner at x=0. D. The function f is differentiable at x=0 because both the left- and right-hand limits of the difference quotient exist at x=0.
1). Does the left-side limit of the difference quotient of the function g(w)=|w| exist at w=0? If it does, write its value in the blank window below. If it does not, write no. 2). Does the right-side limit of the difference quotient of the function g(w)=|w| exist at w=0? If it does, write its value in the blank window below. If it does not, write no. 3). Is the absolute value function g(w) = |w| differentiable at w = 0? Yes or no.
A function is a ratio of quadratic functions and has a verticalasymptote x =4 and just one -intercept, x =1 . It isknown f that has a removable discontinuity at x =- 1 and lim x->-1f(x) = 2. Evaluate a) f (0) b) limx->∞f(x)
Determine whether f is differentiable at x=0 by considering limh→0f(0+h)−f(0) / h. f(x)=7−x Choose the correct answer below. A. The function f is differentiable at x=0 because both the left- and right-hand limits of the difference quotient exist at x=0. B. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient do not exist at x=0. C. The function f is differentiable at x=0 because the graph has a sharp corner at x=0. D. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient exist at x=0, but are not equal.

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