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52-56 Find the limits as x → ∞ and as x → 0o. Use this infor- mation, together with intercepts, to give a rough sketch of the graph as in Example 12. 52. y = 2x3 - x4 53. y

52-56 Find the limits as x → ∞ and as x → 0o. Use this infor- mation, together with intercepts, to give a rough sketch of the graph as in Example 12. 52. y = 2x3 - x4 53. y

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 51E
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(x) 0, lim f(x) = -0, f(2) = 0, || lim f(x) = o, lim f(x) = 0 X3+ x3- 50. Find a formula for a function that has vertical asymptotes x = 1 and x = 3 and horizontal asymptote y = 1. %3D TF 51. A function f is a ratio of quadratic functions and has a ver- tical asymptote x = 4 and just one x-intercept, x = 1. It is known that f has a removable discontinuity at x = -1 and lim,→-1 f(x) = 2. Evaluate (a) f(0) | %3D (b) lim f(x) 52-56 Find the limits as x → ∞ and as x → -00. Use this infor- mation, together with intercepts, to give a rough sketch of the graph as in Example 12. 52. y = 2x3 - x4 53. y = x - x6 %3D | 54. y = x'(x + 2)²(x – 1) 55. y = (3 – x)(1 + x)²(1 – x)* %3D 56. y = x²(x² – 1)²(x + 2) sin x 57. (a) Use the Squeeze Theorem to evaluate lim X→∞ (b) Graph f(x) = (sin x)/x. How many times doag th
Transcribed Image Text:(x) 0, lim f(x) = -0, f(2) = 0, || lim f(x) = o, lim f(x) = 0 X3+ x3- 50. Find a formula for a function that has vertical asymptotes x = 1 and x = 3 and horizontal asymptote y = 1. %3D TF 51. A function f is a ratio of quadratic functions and has a ver- tical asymptote x = 4 and just one x-intercept, x = 1. It is known that f has a removable discontinuity at x = -1 and lim,→-1 f(x) = 2. Evaluate (a) f(0) | %3D (b) lim f(x) 52-56 Find the limits as x → ∞ and as x → -00. Use this infor- mation, together with intercepts, to give a rough sketch of the graph as in Example 12. 52. y = 2x3 - x4 53. y = x - x6 %3D | 54. y = x'(x + 2)²(x – 1) 55. y = (3 – x)(1 + x)²(1 – x)* %3D 56. y = x²(x² – 1)²(x + 2) sin x 57. (a) Use the Squeeze Theorem to evaluate lim X→∞ (b) Graph f(x) = (sin x)/x. How many times doag th
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