Let y = Ae x + Be − x for any constants A , B . (a) Sketch the graph of the function for ( i ) A = 1 , B = 1 ( ii ) A = 1 , B = − 1 ( iii ) A = 2 , B = 1 ( iv ) A = 2 , B = − 1 ( v ) A = − 2 , B = − 1 ( vi ) A = − 2 , B = 1 (b) Describe in words the general shape of the graph if A and B have the same sign. What effect does the sign of A have on the graph? (c) Describe in words the general shape of the graph if A and B have different signs. What effect does the sign of A have on the graph? (d) For what values of A and B does the function have a local maximum ? A local minimum ? Justify your answer using derivatives.
Let y = Ae x + Be − x for any constants A , B . (a) Sketch the graph of the function for ( i ) A = 1 , B = 1 ( ii ) A = 1 , B = − 1 ( iii ) A = 2 , B = 1 ( iv ) A = 2 , B = − 1 ( v ) A = − 2 , B = − 1 ( vi ) A = − 2 , B = 1 (b) Describe in words the general shape of the graph if A and B have the same sign. What effect does the sign of A have on the graph? (c) Describe in words the general shape of the graph if A and B have different signs. What effect does the sign of A have on the graph? (d) For what values of A and B does the function have a local maximum ? A local minimum ? Justify your answer using derivatives.
(
i
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A
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1
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B
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1
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ii
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A
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1
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B
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−
1
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iii
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A
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2
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B
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1
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iv
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A
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2
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B
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−
1
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v
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A
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−
2
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B
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−
1
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vi
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A
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−
2
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B
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1
(b) Describe in words the general shape of the graph if A and B have the same sign. What effect does the sign of A have on the graph?
(c) Describe in words the general shape of the graph if A and B have different signs. What effect does the sign of A have on the graph?
(d) For what values of A and B does the function have a local maximum? A local minimum? Justify your answer using derivatives.
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
I need help making sure that I explain this part accutartly.
Please help me with this question as I want to know how can I perform the partial fraction decompostion on this alebgric equation to find the time-domain of y(t)
Please help me with this question as I want to know how can I perform the partial fraction on this alebgric equation to find the time-domain of y(t)
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