Find the limit. (Hint: Let x = 1/t and find the limit as t→ 0+.) lim 3x tan (²) x →∞0 Step 1 You are asked to find the limit of the function 3x tan as x → ∞o. Attempting to evaluate the limit produces an indeterminate form. Thus, we need to rewrite the function in an equivalent form that the limit can be determined. Substitute x = and find the limit as t→ 0+. 3 tan(8t) lim 3x tan (²) X→∞ = lim t-0+ = lim t-0+ sin(8t) t Submit Skin (you cannot come back)

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Question
Find the limit. (Hint: Let x = 1/t and find the limit as t → 0†.)
8
(²)
Step 1
lim 3x tan
x → ∞
8
as x → ∞. Attempting to evaluate the limit produces an indeterminate form. Thus, we need to rewrite the function in an
X
You are asked to find the limit of the function 3x tan
equivalent form that the limit can be determined.
Substitute x = and find the limit as t → 0+.
Submit
lim 3x tan
X→→∞
8
X
=
=
lim
t→0+
lim
t→0+
Skin (you cannot come back!
3 tan(8t)
sin (8t)
t
3
Transcribed Image Text:Find the limit. (Hint: Let x = 1/t and find the limit as t → 0†.) 8 (²) Step 1 lim 3x tan x → ∞ 8 as x → ∞. Attempting to evaluate the limit produces an indeterminate form. Thus, we need to rewrite the function in an X You are asked to find the limit of the function 3x tan equivalent form that the limit can be determined. Substitute x = and find the limit as t → 0+. Submit lim 3x tan X→→∞ 8 X = = lim t→0+ lim t→0+ Skin (you cannot come back! 3 tan(8t) sin (8t) t 3
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Follow-up Questions
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Follow-up Question
Find the limit. (Hint: Let x = 1/t and find the limit as t → 0+.)
8
an (3)
Step 1
lim 3x tan
X→→∞0
You are asked to find the limit of the function 3x tan
equivalent form that the limit can be determined.
Substitute x =
Submit
and find the limit as t→ 0+.
t
lim 3x tan
X→ ∞
lim
t→0+
Since t → 0+,
8
(³)
Step 2
Rewrite as a product of limits.
sin(8t)
t
=
sin (8t)
t
lim
t→0+
= lim
t → 0+
3
cos(8t)
sin(8t)
t
Skin (you cannot come back)
tan() as x → ∞. Attempting to evaluate the limit produces an indeterminate form. Thus, we need to rewrite the function in an
= lim
t→0+ t
3 tan(8t)
cos (8t)
sin (8t)
and cos(8t) -
3
cos (8t)
3
lim
t→0+ cos(8t)
Transcribed Image Text:Find the limit. (Hint: Let x = 1/t and find the limit as t → 0+.) 8 an (3) Step 1 lim 3x tan X→→∞0 You are asked to find the limit of the function 3x tan equivalent form that the limit can be determined. Substitute x = Submit and find the limit as t→ 0+. t lim 3x tan X→ ∞ lim t→0+ Since t → 0+, 8 (³) Step 2 Rewrite as a product of limits. sin(8t) t = sin (8t) t lim t→0+ = lim t → 0+ 3 cos(8t) sin(8t) t Skin (you cannot come back) tan() as x → ∞. Attempting to evaluate the limit produces an indeterminate form. Thus, we need to rewrite the function in an = lim t→0+ t 3 tan(8t) cos (8t) sin (8t) and cos(8t) - 3 cos (8t) 3 lim t→0+ cos(8t)
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