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Tutorial Exercise Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. tan(8x) lim x 0 sin(7x) Step 1 As x - 0, tan(8x) - 0 and sin(7x) → 0 Step 2 Therefore lim tan(8x) is indeterminate of type We must use l'Hospital's Rule. The derivative of tan(8x) is 8 sec2 (8x) 8 sec2 (87) and the derivative of sin(7x) is x-0 sin(7x) 7 cos( 7x) 7 cos(7r) Step 3 8 sec?(8x) tan(8x) x+0 sin(7x) As x- 0, 8 sec (8x) 7 cos(7x) We have lim = lim x 0 7 cos(7x) Submit Skip (you cannot come back)

Tutorial Exercise Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. tan(8x) lim x 0 sin(7x) Step 1 As x - 0, tan(8x) - 0 and sin(7x) → 0 Step 2 Therefore lim tan(8x) is indeterminate of type We must use l'Hospital's Rule. The derivative of tan(8x) is 8 sec2 (8x) 8 sec2 (87) and the derivative of sin(7x) is x-0 sin(7x) 7 cos( 7x) 7 cos(7r) Step 3 8 sec?(8x) tan(8x) x+0 sin(7x) As x- 0, 8 sec (8x) 7 cos(7x) We have lim = lim x 0 7 cos(7x) Submit Skip (you cannot come back)

Calculus: Early Transcendentals
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...
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Tutorial Exercise Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. tan(8x) lim x→0 sin(7x) Step 1 As x → 0, tan(8x) · and sin(7x) - Step 2 tan(8x) Therefore lim is indeterminate of type . We must use l'Hospital's Rule. The derivative of tan(8x) is 8 sec (8x) 8 sec?(8r) and the derivative of sin(7x) is x → 0 sin(7x) 7 cos (7x) 7 cos(7r) Step 3 8 sec?(8x) 7 cos(7x) tan(8x) 8 sec-(8x), As x → 0, We have lim x →0 sin(7x) lim x →0 7 cos(7x) Submit Skip (you cannot come back)
Transcribed Image Text:Tutorial Exercise Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. tan(8x) lim x→0 sin(7x) Step 1 As x → 0, tan(8x) · and sin(7x) - Step 2 tan(8x) Therefore lim is indeterminate of type . We must use l'Hospital's Rule. The derivative of tan(8x) is 8 sec (8x) 8 sec?(8r) and the derivative of sin(7x) is x → 0 sin(7x) 7 cos (7x) 7 cos(7r) Step 3 8 sec?(8x) 7 cos(7x) tan(8x) 8 sec-(8x), As x → 0, We have lim x →0 sin(7x) lim x →0 7 cos(7x) Submit Skip (you cannot come back)
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