d. The number 1 raised to any fixed power is 1. Therefore, because (1+x)→1 as x→0, (1 +x)* →1 as x→0. Is the statement true or false? Explain.1O A.True; the limit of (1+x)* as x-→0 is 1.O B. False; the limit is in the indeterminate form 10O C. False; the limit is in the indeterminate form 00O D. False; the limit is in the indeterminate form ooe. The functions In x00 and Inx have comparable growth rates as x+0o. Is the statement true or false? Explain.• 100x99*100= limIn x 100O A. True; by l'Hôpital's Rule, limInx= lim 100 = 100.1X00X00X00O B. False; sinceInx10000is in the indeterminate formthe functions do not have comparable growth rates.Inx001• 100x99x100O C. False; by l'Hôpital's Rule, lim100Inx'= lim= lim x= o0.In x1X00X00X00In xO D. False; lim100= In x99.= 0o.In xX00f. The function ex grows faster than 2* as x→0o. Is the statement true or false? Explain.O A. True; lim2*= lim= 0.eX00 ex00O B. False; limex= lim= 00.X00x002*In 2.2*O C. False; by l'Hôpital's Rule, limso relative growth rates are impossible to determine.= limX0o eX00O D. False; the growth rates are comparable since lim2* 2eX00 e Determine whether the following statements are true and give an explanation or counterexample.х-2-= limx→2x² - 11 1a. By l'Hôpital's Rule, limIs the statement true or false? Explain.4-- -X-22xO A. True; l'Hôpitaľ's Rule is applied correctly.х-2x-2O B. False; the expressionx-1is not indeterminate, lim= 0.22X-2x - 1x-21 1OC. False; by l'Hôpital's Rule, lim= limX-2x- 12X2 Xх-2is not indeterminate, limx - 1х-21O D. False; the expression2X-2x -13b. Is lim (x sin x) = lim f(x)g(x) = lim f'(x) lim g'(x) = ( lim 1)( lim cos x) = 1 a true or false statement? Explain.x-0x-0x-0O A. True; l'Hôpitaľ's Rule is applied correctly.O B. False; the expression (x sin x) is not indeterminate, lim (x sin x) = 0.OC.1False, lim (x sin x) = lim f(x)g(x) = lim f'(x) lim g'(x) = ( lim 1)( lim cos x)%3Dx-0x-0x-0O D. False; the expression (x sin x) is not indeterminate, lim (x sin x) = - 1.limx* is an indeterminate form. Is the statement true or false? Explain.c.O A. True; the limit is in the indeterminate form 00.1O B. False, limx* = 0.1OC. False, limX= 1.O D. False, lim= 00.

d. The number 1 raised to any fixed power is 1. Therefore, because (1+ x)→1 as x→0, (1 + x) * →1 as x→0. Is the statement true or false? Explain. O A. True; the limit of (1+ x)* as x→0 is 1. O B. False; the limit is in the indeterminate form 10. OC. False; the limit is in the indeterminate form 00. O D. False; the limit is in the indeterminate form o0.

d. The number 1 raised to any fixed power is 1. Therefore, because (1+ x)→1 as x→0, (1 + x) * →1 as x→0. Is the statement true or false? Explain. O A. True; the limit of (1+ x)* as x→0 is 1. O B. False; the limit is in the indeterminate form 10. OC. False; the limit is in the indeterminate form 00. O D. False; the limit is in the indeterminate form o0.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

If limx→0(2f(x)−15)=45limx→0(2f(x)−15)=45, then what must limx→0f(x)limx→0f(x) equal?
Use the –δ definition to prove that lim x→1 (3x + 5)/2 = 4.
Evaluate in terms of the constant a. lim (2a + x) x→ 0
Evaluate lim (x,y) ---> (0,0) (2xy^2)/(3x^2+3y^2)
Prove, using the formal definition, that limx→ 8 [(x)^1/3 = 2.]
Suppose that limx→0f(x)=π. Select the best answer below. 3.14<f(x)<π on some interval (−δ,δ) 3.14<f(x)<3.153.14 on the interval (−10−15,10−15) 3.14<f(x)<3.153.14 on some interval (−δ,δ) π<f(x)<3.15 on some interval (−δ,δ)
Suppose that limx→2[f(x)+x2]=α. Find limx→1(x+1)f(2x) 2α−4 Not applicable 2f(2) 2(α−4)
Prove using the formal definintion of a function that: limxto2 (5x + 5) = 15
what is lim of x approaches -8 from the left of 7x+56/abolute value of x+8
Is it possible for f(1) = 3 and limx→1 f(x) = 5? Explain.
Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a exist otherwise enter 0.
If (x, y)lim(2, 3) f(x, y) = 4, can you conclude anything about f(2, 3)? Explain.