Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Concept explainers

LUP Decomposition
LU decomposition stands for Lower-Upper decomposition. LU decomposition is the factorization of the lower triangular matrix and an upper triangular matrix. It is very useful in linear algebra and numerical analysis. A permutation matrix is usually inclu…
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I have the question and the answer for this problem I just want to understand the concepts and logic of how to do it step by step

 

LUsing Taylor's thearem, we can obtain a formula to calculate he sine of S sin(x) - x - + (-1) (2n - 1)! Write a function detinition to calculate the sine of x using the formula above. Your function should teminate when the absolute value of the last term calculated is less than 1.0 x 10. You may not use any functions supplied in the cmath.h header file (ie. you cannor use the powx.y) function Your sine function may call other functions, and in this case, you must also wrie the definitions of those functions. You do nor need to comment anything, although, a well-placed comment may provide clarity for the grader. Bonus (2 pes): Briefly explain why the sine function above will always converge. You will only get the bonus points if the sine function is wrimen. Single Function Version Multiple Function Version double sin(double x) ( int i; int n- 1 int sign; double eps - 1.De-4; double sum- 0.0; double pow; lang fact; double this term; do { pow - 1.0; Pact- 1 for (1-1; ie-2*n-1; +1) { double sint double x) ( int a- 1; double eps - 1.0e-4; double sum - 0.0; double this tera do this tern-sign(n-1)"pow(x, 2"a- 1)/fact(2'n-1): sum this tern; ir (this tern <0.0) this tern - -this term; *n; } while (this tern eps); return sum; pow x; fact i ir ((n-aa - 1) sign --1; else sign - 1; this tern- sign'pow/fact; int sign(int n) { if (ns2 -- 1) return -1 return 1; sum - this_term; if (this_ter < 0.0) this tern --this term double powdouble K, int a) { int A double p- 1.0 for (i-0; ien; **1) } while (this tera eps): Feturn sim; P- x; return p: lang fact (int n) { int i; long f-1 for (1-1; ien; 1) { return f
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Transcribed Image Text:LUsing Taylor's thearem, we can obtain a formula to calculate he sine of S sin(x) - x - + (-1) (2n - 1)! Write a function detinition to calculate the sine of x using the formula above. Your function should teminate when the absolute value of the last term calculated is less than 1.0 x 10. You may not use any functions supplied in the cmath.h header file (ie. you cannor use the powx.y) function Your sine function may call other functions, and in this case, you must also wrie the definitions of those functions. You do nor need to comment anything, although, a well-placed comment may provide clarity for the grader. Bonus (2 pes): Briefly explain why the sine function above will always converge. You will only get the bonus points if the sine function is wrimen. Single Function Version Multiple Function Version double sin(double x) ( int i; int n- 1 int sign; double eps - 1.De-4; double sum- 0.0; double pow; lang fact; double this term; do { pow - 1.0; Pact- 1 for (1-1; ie-2*n-1; +1) { double sint double x) ( int a- 1; double eps - 1.0e-4; double sum - 0.0; double this tera do this tern-sign(n-1)"pow(x, 2"a- 1)/fact(2'n-1): sum this tern; ir (this tern <0.0) this tern - -this term; *n; } while (this tern eps); return sum; pow x; fact i ir ((n-aa - 1) sign --1; else sign - 1; this tern- sign'pow/fact; int sign(int n) { if (ns2 -- 1) return -1 return 1; sum - this_term; if (this_ter < 0.0) this tern --this term double powdouble K, int a) { int A double p- 1.0 for (i-0; ien; **1) } while (this tera eps): Feturn sim; P- x; return p: lang fact (int n) { int i; long f-1 for (1-1; ien; 1) { return f
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