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Question 4.21) Evaluate the following limits. sin² (1)-1 1-4 A) lim 2/2+1 B) lim x-0 Question 4.22) Evaluate the following limits. A) lim x(arctan(x)-E) 110 1-cos(2x) x² B) lim x x-0° C) lim 004--1 x ln(x) x² + 1 C) lim (1+sin())* 4x²-12x+9 x-½ 2x²-x-3 D) lim Question 4.31) Consider f(x)=x² and h(x) = 4x-4. A) Sketch the graph of these on the interval x= [0,3]. (Draw the two curves on the same figure.) B) Suppose that there is some function g(x) satisfying f(x) ≥g(x) > h(x) for all x. What is lim g(x)? (Invoke a certain theorem... which?)

Question 4.21) Evaluate the following limits. sin² (1)-1 1-4 A) lim 2/2+1 B) lim x-0 Question 4.22) Evaluate the following limits. A) lim x(arctan(x)-E) 110 1-cos(2x) x² B) lim x x-0° C) lim 004--1 x ln(x) x² + 1 C) lim (1+sin())* 4x²-12x+9 x-½ 2x²-x-3 D) lim Question 4.31) Consider f(x)=x² and h(x) = 4x-4. A) Sketch the graph of these on the interval x= [0,3]. (Draw the two curves on the same figure.) B) Suppose that there is some function g(x) satisfying f(x) ≥g(x) > h(x) for all x. What is lim g(x)? (Invoke a certain theorem... which?)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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Can you please answer question 4.22
Question 4.11) Compute the following limits at infinity. x²-x53 +1 A) lim x+2 x³ + 2x D) lim 007-1 -5) 1¹/² x=3 A) lim Chapter 4: LIMITS (SECOND PART) B) lim-10√x Question 4.21) Evaluate the following limits. sin² (t)-1 1-2/2 1-4 X-00 Question 4.12) Find horizontal asymptotes, if any, for the following. A) y= f(x)= x³ + 3x-5 2x² + 3x³ B) y(x)=- +x Careful: In only one of the above cases should you have the same HA line on both sides. E) lim ²- +3t² 100 L Question 4.22) Evaluate the following limits. A) lim x(arctan(x)-) B) lim x-0 B) lim xx x-0* X 1-cos(2x) x² 2 C) lim- B) lim- x2 cos(x)+9x C) lim What is lim g(x)? (Invoke a certain theorem... which?) x-2 2x+3 √√√x²-x x ln(x) x² +1 C) lim (1+sin())* Question 4.31) Consider f(x)=x² and h(x) = 4x-4. A) Sketch the graph of these on the interval x= [0,3]. (Draw the two curves on the same figure.) B) Suppose that there is some function g(x) satisfying f(x) ≥ g(x) > h(x) for all x. Question 4.32) Use the Squeeze Theorem to compute the following limits. Show all your steps. 3x A) lim sin(3t+1) 1² 4x²-12x+9 D) im 2x²-x-3 C) lim √ sin 1-0* sin (1/²) D) lim tan ¹ (sin x) √x
Transcribed Image Text:Question 4.11) Compute the following limits at infinity. x²-x53 +1 A) lim x+2 x³ + 2x D) lim 007-1 -5) 1¹/² x=3 A) lim Chapter 4: LIMITS (SECOND PART) B) lim-10√x Question 4.21) Evaluate the following limits. sin² (t)-1 1-2/2 1-4 X-00 Question 4.12) Find horizontal asymptotes, if any, for the following. A) y= f(x)= x³ + 3x-5 2x² + 3x³ B) y(x)=- +x Careful: In only one of the above cases should you have the same HA line on both sides. E) lim ²- +3t² 100 L Question 4.22) Evaluate the following limits. A) lim x(arctan(x)-) B) lim x-0 B) lim xx x-0* X 1-cos(2x) x² 2 C) lim- B) lim- x2 cos(x)+9x C) lim What is lim g(x)? (Invoke a certain theorem... which?) x-2 2x+3 √√√x²-x x ln(x) x² +1 C) lim (1+sin())* Question 4.31) Consider f(x)=x² and h(x) = 4x-4. A) Sketch the graph of these on the interval x= [0,3]. (Draw the two curves on the same figure.) B) Suppose that there is some function g(x) satisfying f(x) ≥ g(x) > h(x) for all x. Question 4.32) Use the Squeeze Theorem to compute the following limits. Show all your steps. 3x A) lim sin(3t+1) 1² 4x²-12x+9 D) im 2x²-x-3 C) lim √ sin 1-0* sin (1/²) D) lim tan ¹ (sin x) √x
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