Higher Engg Maths- 4 Errors, Study notes of Engineering Mathematics

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ERRORS 4.1 ERROR DETERMINATION We know that lim by ar 0 Ox ax a d ve a approximatcly => we a 5x approximaicly ox dx dx 'y Definition, () 8x is known as absolute error in x. bx Gi). is known as relative error in x. Git) (*) x100 is known as percentage error in x. Example 1, Find the percentage error in the area of a rectangle when an error of +1 percent is made in measuring its length and breadth (R.GPV, Bhopal, June 2008, 2004) Solution, Let A be the area and /, 5, be the length and breadth respectively, Arca of the rectangle, A ib Taking log of both the sides, we have log A = log /+ log b - ) Differentiating equation (1), we get 64 _ 8 88 uy Ail ob 84 8 8b => 100 =1007-+100-- = +1 +1= +2 Hence, percentage error in area = + 2 Ans. 2 Example 2. The power dissipated in a resistor is given by P = =. Find by using calculus the approximate percentage change in P when Fis increased by 3% and R is decreased by 2%, (A.M.LE. Summer 2001) . 100 5E 100 5R Solution. Here, we have = 3% and RR -2% pe P= RR => log P=2 log F- log Rk On differentiating, we get SP 100SE 1008R OP _ 2 5p BRL, typ SP eo, - Pp E R P E R 87