By C. B. Gupta
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Extra resources for Advanced Mathematics
I) 2 sinh F b I cosh F a + b + bxI H 2K H 2 K (ii) F H (iv) h – 2 sin x + (iii) – cosec 2x+1 F H (v) 2hx + h2 + ex(eh – 1) LM N F H (vi) log 1 + I K (vii) eax e ah log 1 + h + (e ah − 1) log bx x OP Q (viii) 4. (i) – 4 sin2 h cos (2x + 2h) (iv) + 2hx + 2h – I K 4 6 + ( x + 2) ( x + 3) ( x + 4) ( x + 3) ( x + 4) ( x + 5) (ii) 2 sin (iii) 720 abc 8. (i) I sin F h I K H 2K h(2 x + h ) cos 2 x + 2 x 2 sin h sin (2 x + h ) cos (2 x + 2 h ) cos 2 x F H ( − 1)n n ! x ( x + 1) ( x + 2 ) ...... ( x + n ) 5h2 h x h 2 (ii) (bc – 1)2 abcx (iii) 6x 5.
Ann x n = bn Above equation can be written as x1 = U| || V| || W 1 [b1 − a12 x2 − a13 x 3 ...... a1n xn ] a11 x2 = 1 [b2 − a 21 x 1 − a23 x 3 ...... a 2 n x n ] a22 x3 = 1 [b3 − a31 x1 − a 32 x 2 ...... a3 n x n ] a33 . : xn = 1 [bn − a n1 x1 − a n 2 x 2 ...... S. 6), we get x1( 2 ) = 1 [b1 − a12 x 2(1) − a13 x3(1) ...... a1n x n(1) ] a11 45 SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS Now put x1( 2 ) x 2(1) x 3(1) ...... S. 6), we get x 2( 2 ) = 1 [b2 − a21 x1( 2 ) − a23 x 3(1) ...... 6), we get x 3( 2 ) = 1 [ b3 − a31 x1( 2 ) − a32 x 2( 2 ) ......
A1n x n = b1 a21 x1 + a22 x 2 + ...... + a2 n x n = b2 . . : : : : am1 x1 + am 2 x 2 + ...... 1) Step 1. To eliminate x1 from the second, third .... nth equation a21 times the a11 first equation from the second equation, similarly we eliminate x1 from third equation by subtracting a31 times the first equation from the third equation, etc. We get new system of equation as a11 a11 x1 + a12 x 2 + ...... + a1n x n = b1 b22 x 2 + ...... + b2 n x n = b2′ b32 x 2 + ...... 2) . . : : : bm 2 x 2 + ......
Advanced Mathematics by C. B. Gupta