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Calculate these limits. If the limit is ∞ or -∞, write infinity or-infinity. If the limit does not exist, write DNE: Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator. 1. If the denominator does not go to 0, you should be able to right down the answer immediately. 2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (±) of the quotient, from both sides if the limit is not one-sided. 3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing. So, group your limits into these three forms and work with them one group at a time. (a) lim t-pi/2 sint-√ sin 2t+14cos ² t 7 2 2 2cos t (b) lim sint + sin 2t+14cos = ∞ t-pi/2 2 2cos t (c) lim cost-√sin 2t+14cos² t = t-pi/2 2cos t (d) lim t→pi/2 cost+√ sin t + 14cos 2cos ² t = ∞ (e) lim sint-v sin 2 t + 14cos = 0 t-pi/2 (f) lim t-pi/2 sin t +√ sin 2sin 2 t 2 t + 14cos t 2sin t cost- (g) lim sin 2 t + 14cos t-pi/2 (h) lim t-pi/2 2sin 2 t cost + sin 2t+14cos 2 2sin t (i) lim sin t -v sin t-pi/2 t + 14 cos² + 2cos t = (i) lim t-pi/2 sin t +√ sin 2cos t 2 t + 14cos ² t = (k) lim cost-V sin 2 t-pi/2 t + 14cos 2cos t (1) lim cost+v sin 2 t + 14cos t-pi/2 2cos t

Calculate these limits. If the limit is ∞ or -∞, write infinity or-infinity. If the limit does not exist, write DNE: Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator. 1. If the denominator does not go to 0, you should be able to right down the answer immediately. 2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (±) of the quotient, from both sides if the limit is not one-sided. 3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing. So, group your limits into these three forms and work with them one group at a time. (a) lim t-pi/2 sint-√ sin 2t+14cos ² t 7 2 2 2cos t (b) lim sint + sin 2t+14cos = ∞ t-pi/2 2 2cos t (c) lim cost-√sin 2t+14cos² t = t-pi/2 2cos t (d) lim t→pi/2 cost+√ sin t + 14cos 2cos ² t = ∞ (e) lim sint-v sin 2 t + 14cos = 0 t-pi/2 (f) lim t-pi/2 sin t +√ sin 2sin 2 t 2 t + 14cos t 2sin t cost- (g) lim sin 2 t + 14cos t-pi/2 (h) lim t-pi/2 2sin 2 t cost + sin 2t+14cos 2 2sin t (i) lim sin t -v sin t-pi/2 t + 14 cos² + 2cos t = (i) lim t-pi/2 sin t +√ sin 2cos t 2 t + 14cos ² t = (k) lim cost-V sin 2 t-pi/2 t + 14cos 2cos t (1) lim cost+v sin 2 t + 14cos t-pi/2 2cos t

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.CT: Chapter Test
Problem 14CT: A bottle of medicine is to be stored at a temperature between 5 C and 10 C. What range does this...
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Calculate these limits. If the limit is ∞ or -∞, write infinity or-infinity. If the limit does not exist, write DNE: Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator. 1. If the denominator does not go to 0, you should be able to right down the answer immediately. 2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (±) of the quotient, from both sides if the limit is not one-sided. 3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing. So, group your limits into these three forms and work with them one group at a time. (a) lim t-pi/2 sint-√ sin 2t+14cos ² t 7 2 2 2cos t (b) lim sint + sin 2t+14cos = ∞ t-pi/2 2 2cos t (c) lim cost-√sin 2t+14cos² t = t-pi/2 2cos t (d) lim t→pi/2 cost+√ sin t + 14cos 2cos ² t = ∞ (e) lim sint-v sin 2 t + 14cos = 0 t-pi/2 (f) lim t-pi/2 sin t +√ sin 2sin 2 t 2 t + 14cos t 2sin t cost- (g) lim sin 2 t + 14cos t-pi/2 (h) lim t-pi/2 2sin 2 t cost + sin 2t+14cos 2 2sin t (i) lim sin t -v sin t-pi/2 t + 14 cos² + 2cos t = (i) lim t-pi/2 sin t +√ sin 2cos t 2 t + 14cos ² t = (k) lim cost-V sin 2 t-pi/2 t + 14cos 2cos t (1) lim cost+v sin 2 t + 14cos t-pi/2 2cos t
Transcribed Image Text:Calculate these limits. If the limit is ∞ or -∞, write infinity or-infinity. If the limit does not exist, write DNE: Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator. 1. If the denominator does not go to 0, you should be able to right down the answer immediately. 2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (±) of the quotient, from both sides if the limit is not one-sided. 3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing. So, group your limits into these three forms and work with them one group at a time. (a) lim t-pi/2 sint-√ sin 2t+14cos ² t 7 2 2 2cos t (b) lim sint + sin 2t+14cos = ∞ t-pi/2 2 2cos t (c) lim cost-√sin 2t+14cos² t = t-pi/2 2cos t (d) lim t→pi/2 cost+√ sin t + 14cos 2cos ² t = ∞ (e) lim sint-v sin 2 t + 14cos = 0 t-pi/2 (f) lim t-pi/2 sin t +√ sin 2sin 2 t 2 t + 14cos t 2sin t cost- (g) lim sin 2 t + 14cos t-pi/2 (h) lim t-pi/2 2sin 2 t cost + sin 2t+14cos 2 2sin t (i) lim sin t -v sin t-pi/2 t + 14 cos² + 2cos t = (i) lim t-pi/2 sin t +√ sin 2cos t 2 t + 14cos ² t = (k) lim cost-V sin 2 t-pi/2 t + 14cos 2cos t (1) lim cost+v sin 2 t + 14cos t-pi/2 2cos t
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