A textbook of Computer Based Numerical and Statiscal Techniques part 3 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 3 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 3 ppsx

... Approximate value (x′) = 0 .33 3 Therefore, Absolute Error, 1 0 .33 3 0 .33 333 3 0 .33 3 0.00 033 3 3 a Exx ′ =− =− = − = Relative Error, E r = 0.00 033 3 0.000999 0 .33 333 3 a E x == and Percentage Error, E p = ... second decimal places. Example 4. If 0 .33 3 is the approximate value of 1 3 , then find its absolute, relative and percentage errors. Sol. Given that True val...
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A textbook of Computer Based Numerical and Statiscal Techniques part 2 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 2 ppsx

... problems. A major advantage for numerical technique is that a numerical answer can be obtained even when a problem has no analytical solution. However, result from numerical analysis is an approximation, in ... significant figures at each step of computation. At each step of computations, retain at least one more significant figure than that given in the data, perform the last...
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A textbook of Computer Based Numerical and Statiscal Techniques part 5 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 5 ppsx

... obtained by x 1 = 2 22 44 and 22 bb ac bb ac aa −+ − −− − =x These are called closed form solution. Similar formulae are also available for cubic and biquadratic polynomial equations but we rarely ... 26 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES The basic operations specified by IEEE arithmetic are first and foremost addition, subtraction, multiplication, and divi...
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A textbook of Computer Based Numerical and Statiscal Techniques part 14 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 14 ppsx

... 122 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 22. Evaluate: ∆ n [sin (ax + b)] Sol. We know f∆ (x) = f(x + h) – f (x) therefore ∆ sin (ax + b) = sin [a (x + h)+b] – sin)(ax ... hD hD hD 116 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 14. Evaluate the following: I. ∆ 2 (cos 2x) II. ∆ 2 (3e x ) III. ∆ tan –1 x IV. ∆(x + cos x) the inte...
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A textbook of Computer Based Numerical and Statiscal Techniques part 16 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 16 ppsx

... 22 1 2 n nn an bn c n a n b n a n  − −++−∆+∆+∆   142 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 9. Evaluate the production of wool in the year 1 935 from the given data: ( ) 1 931 1 932 1 933 ... given a set of equidistant values of arguments and its corresponding value of f(x). Suppose for n + 1 equidistant argument values x = a, a + h, a + 2h,...
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A textbook of Computer Based Numerical and Statiscal Techniques part 17 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 17 ppsx

... R.H.S. 3. 9 FACTORIAL NOTATIONS The product of n consecutive factors each at a constant difference and the first factor being x is called a factorial function or a factorial polynomial of degree n and ... n C 3 x 3 E 3 + ]u 0 = u 0 + n C 1 u 1 x + n C 2 u 2 x 2 + n C 3 u 3 x 3 + = L.H.S. 150 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES CorCor...
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A textbook of Computer Based Numerical and Statiscal Techniques part 25 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 25 ppsx

... the Lagrange’s formula is y x = ()()() ()() () ()()() () ()() 53 335 535 5 3 5 3 55 35 33 35 xxx xxx yy −− +−− +−− + −+ −− −− −+ −− −− + ()()() ()()() ()()() ()()() 35 535 533 533 335 55 535 3 xxx ... using Lagrange’s interpolation formula. Sol. We are given () :78910 :31 1 9 x fx 226 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 1. Using Lagrange’s f...
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A textbook of Computer Based Numerical and Statiscal Techniques part 26 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 26 ppsx

... life. [Ans. 15.67] 13. Find the value of tan 33 ° by Lagrange’s formula if tan 30 ° = 0.5774, tan 32 ° = 0.6249, tan 35 ° = 0.7002, tan 38 ° = 0.78 13. [Ans. 0.64942084] 14. Apply Lagrange’s formula to ... n ax ax ax ax −− −− 11. Certain corresponding values of x and log 10 x are given as 10 : 30 0 30 4 30 5 30 7 log : 2.4771 2.4829 2.48 43 2.4871 x x Find the log 10 30 1...
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A textbook of Computer Based Numerical and Statiscal Techniques part 29 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 29 ppsx

... co-efficients a 1 , a 2 a n will produce little error for small x near zero. But probably substantial error near the ends of the interval 268 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 7. Apply ... approximation to a given function. For evaluating a function f(x) on a computer it is generally more efficient of space and time to have an analytic approxi...
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A textbook of Computer Based Numerical and Statiscal Techniques part 51 ppsx

A textbook of Computer Based Numerical and Statiscal Techniques part 51 ppsx

... 0.5 230 cm. and a standard deviation of 0.0 032 cm. Calculate the 2-sigma and 3- sigma upper and lower control limits for mean of sample of 4. Ans. 2–sigma UCL 0.5262 cm LCL 0.5198 cm CL 0.5 230 ... concern has an average sale of Rs. 10000/- daily estimated over a long period. A salesman claims that he will increase the average sales by Rs. 700/- a day. The concern is...
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