9396867
Description
Quiz by India Rose, updated more than 1 year ago
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Created by India Rose
about 7 years ago
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Question 1
Question
Wie wird die partielle Integration richtig durchgeführt?
Answer
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∫ ( f(x) * g'(x) ) dx = f(x) * g(x) - ∫ ( f'(x) * g(x) ) dx
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∫ ( f(x) * g'(x) ) dx = f(x) * g(x) + ∫ ( f'(x) * g(x) ) dx
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∫ ( f(x) * g'(x) ) dx = f(x) * g(x) - ∫ ( f(x) * g(x) ) dx
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∫ ( f(x) * g(x) ) dx = f(x) * g(x) - ∫ ( f'(x) * g(x) ) dx
Question 2
Question
Wie lautet die Formel zur Berechnung von ak?
Answer
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ak = (π / 2) (-π)∫(π) ( f(x) * cos(k*x ) ) dx
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ak = (1 / π) (-e)∫(π) ( f(x) * cos(k*x ) ) dx
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ak = (1 / π) (-π)∫(π) ( f(x) * cos(k*x ) ) dx
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ak = (1 / π) (-π)∫(π) ( f(x) * sin(k*x ) ) dx
Question 3
Question
Wie lautet die Formel zur Berechnung von bk?
Answer
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bk = (1 / π) (-π)∫(π) ( f(x) * sin(e*x ) ) dx
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bk = (1 / π) (-π)∫(π) ( f(x) * sin(k*x ) ) dx
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bk = (π / 2) (-π)∫(π) ( f(x) * sin(k*x ) ) dx
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bk = (1 / π) (-π)∫(π) ( -f(x) * -sin(k*x ) ) dx
Question 4
Question
Die Formel von a0 lautet wie folgt: ak = (1 / π[blank_start])[blank_end]
Answer
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) (-π)∫(π) ( f(x) * cos(k*x) ) dx
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) (-π)∫(-π) ( -f(x) ) dx
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) (-π)∫(π) ( -f(x) ) dx
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) (-π)∫(π) ( f(x) ) dx
Question 5
Question
Wie lautet die Formel für die Fourieranalyse?
Answer
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f(x) = (a0 / 2) + (∞)∑ (k=1) ( (ak * cos(k*x) + bk *sin(k*x) )
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f(x) = (a0 / 2) + (∞)∑ (k=1) ( (bk * cos(k*x) + ak *sin(k*x) )
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f(x) = (a0 / 2) + (∞)∑ (k=1) ( (ak * sin(k*x) + bk *sin(k*x) )
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f(x) = (a0 / 2) - (∞)∑ (k=1) ( (ak * cos(k*x) - bk *sin(k*x) )
Question 6
Question
Wie lautet die summierte Rechtecksformel?
Answer
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∫ ( f(x) ) dx = (( b - a ) / n ) * f(x0) + ... + (( b - a ) / n ) * f(xn-1)
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∫ ( f(x) ) dx = (( b - a ) / n ) * f(x0) + ... + (( a - b ) / n ) * f(xn-1)
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∫ ( f(x) ) dx = (( b - a ) / n ) * f(x0) + ... + (( b - a ) / n ) * f(xn)
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∫ ( f(x) ) dx = (( b - a ) / b ) * f(x0) + ... + (( b - a ) / n ) * f(xn-1)
Question 7
Question
Wie lautet die Trapezformel?
Answer
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∫ ( f(x) ) dx = ( b - a ) * (( f(a) + f(b) ) / 2 )
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∫ ( f(x) ) dx = ( a - b ) * (( f(a) + f(b) ) / 2 )
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∫ ( f(x) ) dx = ( b - a ) * (( f(a) + f(b) ) / 4 )
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∫ ( f(x) ) dx = ( b - a ) * (( f(n) + f(a) ) / 2 )
Question 8
Question
Wie lautet die Simpsonregel ? (Summierte Kepplersche Fassregel?)
Answer
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∫ ( f(x) ) dx = (( b - a ) / (6*n)) * ( f(x0) + 4 * f(x1) + 2 * f(x2) + 4 * f(x3) + ... + 2 * f(x2n-2) + 4 * f(x2n-1) + f(x2n) )
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∫ ( f(x) ) dx = (( a - b ) / (6*n)) * ( f(x0) + 4 * f(x1) + 2 * f(x2) + 4 * f(x3) + ... + 2 * f(x2n-2) + 4 * f(x2n-1) + f(x2n) )
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∫ ( f(x) ) dx = (( b - a ) / (2*n)) * ( f(x0) + 4 * f(x1) + 2 * f(x2) + 4 * f(x3) + ... + 2 * f(x2n-2) + 4 * f(x2n-1) + f(x2n) )
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∫ ( f(x) ) dx = (( b - a ) / (6*n)) * ( f(x0) + 4 * f(x1) + 2 * f(x2) + 4 * f(x3) + ... + 2 * f(xn-2) + 4 * f(xn-1) + f(xn) )
Question 9
Question
Wie berechnet sich die Bogenlänge von Kurven?
Answer
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L = √( ( f(b) + f(a) )² + ( g(b) + g(a) )² )
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L = √( ( f(b) - f(a) )² - ( g(b) - g(a) )² )
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L = √( ( f(b) - f(b) )² + ( g(a) - g(a) )² )
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L = √( ( f(b) - f(a) )² + ( g(b) - g(a) )² )
Question 10
Question
Wie berechnet man den nächsten Schritt im De Casteljau Algorithmus?
Answer
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( 1 - t ) * P0 + t * P1
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( 1 - t ) * P1 - t * P0
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t * P0 + (1 - t ) * P1
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t * P0 + t * P1
Question 11
Question
Wie funktioniert das Newton-Verfahren?
Answer
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g(x) = x * (f(x)/f'(x))
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g(x) = x / (f(x)/f'(x))
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g(x) = x + (f(x)/f'(x))
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g(x) = x * (F(x)/f'(x))
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