zakinutuzi

zakinutuzi

Answered

2021-12-17

Find a region whose size matches the specified limit. Do not evaluate the limit. lim x tends to infinity summation π4n×taniπ4n

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Answer & Explanation

Philip Williams

Philip Williams

Expert

2021-12-18Added 39 answers

Step 1 
Remember that 
abf(x) dx =limnΔxi=1nf(a+iΔx) 
Where Δx=ban 
Step 2 
limni=1nπ4ntan(iπ4n) 
Comparing shows that
Δx=π4n 
a=0 
Δx=ban=π4nb=π4 
and f(x)=tanx 
Therefore, 
limni=1ntan(iπ4n)=0π4tanx dx  
We determine that 
This sum represent the area under the curve y=tanx and above x-axis in the interval x[0. π4] 
The sum represent the area of the blue region in the graph below: 

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ol3i4c5s4hr

ol3i4c5s4hr

Expert

2021-12-19Added 48 answers

Solution: 
Given: limni=1nπ4ntanπ4n 
=0π4tanx dx  
f(x)=tanx, x[0, π4]

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