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A textbook of Computer Based Numerical and Statiscal Techniques part 6 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 6 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 6 pptx

... between 0 .65 7 and 0 .66 5.Eighth approximation: The eighth approximation to the root is given by 80 .65 7 0 .66 50 .66 12x+==From last two approximations, i.e.,70 .6 65x= and 80 .6 61x= ... positive.Therefore f (0 .67 3) is positive and f(0 .65 7) is negative so the root lies between 0 .65 7 and 0 .67 3.ALGEBRAIC AND TRANSCENDENTAL EQUATION41Seventh approximation: The seventh approximation to the ... (approximation) a and b (where (a > b)) such thatf (a) . f(b) < 0.Step 2: Evaluate the mid point x1 of a and b given by x1 = 12 (a + b) and also evaluatef(x1).Step 3: If f (a) ....
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A textbook of Computer Based Numerical and Statiscal Techniques part 19 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 19 pptx

... the argument half waybetween the arguments at q and r is +B A, 24 where A is the arithmetic mean of q and r and B is arithmeticmean of 3q – 2p – s and 3r – 2s – p.Sol. Given A is the arithmetic ... r and s corresponds to argument a, a + h, a + 2h and a + 3h respectivelythen the value of the argument lying half way between a + h and a + 2h will be a + h + 2h i.e., a + 32hHence ,a ... series of which 23 .6 is the6th term. Find the first and tenth terms of the series.xy34 5 6 7 8 94.8 8.4 14.5 23 .6 36. 2 52.8 73.9174 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES (a) Here,...
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A textbook of Computer Based Numerical and Statiscal Techniques part 20 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 20 pptx

... 18) 26 −− −−×− + ×−= 235 – 24 .65 – 10. 766 25 – 1.0 766 25= 235 – 36. 492875= 198.507 { 198∴ Total no. of candidates who obtained fewer than 70 marks are 198.Example 6. The area A of a circle of ... of candidates who obtained marks between certain limitsare as follows:MarksNo of candidates−−−−−0192039405 960 798099. 41 62 65 50 17Find no. of candidates who obtained fewer than 70 marks.Sol. ... maturing at the age of 63 :45 50 55 60 65 ( .) 114.84 96. 16 83.32 74.48 68 .48AgePremium in Rs[Ans. 70.585152] 6. The values of annuities are given for the following ages. Find the value of annuity...
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A textbook of Computer Based Numerical and Statiscal Techniques part 30 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 30 pptx

... dxa xdxa xdxa xdx 111135/2 2 40120000x dxa xdxa xdxa xdx=++∫∫∫∫or Simplifying above equations, we get12001201222332234523457aa a aaaaaa++=++ =++=284 COMPUTER BASED NUMERICAL ... NUMERICAL AND STATISTICAL TECHNIQUES Minimax polynomial approximation: Let f(x) be continuous on [a, b] and it isapproximated by the polynomial Pn (x) = a 0 + a 1x + +a nxn , then the minimax ... bnnaa a a a wxdx a xwxdx a xwxdx wxfxdx() () () () ()2101 bb b bnnaa a a a xw x dx a x w x dx a x w x dx xw x f x dx++++ =∫∫ ∫ ∫() () () ()()1201 bb bbnnnnnaa aa a x w...
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A textbook of Computer Based Numerical and Statiscal Techniques part 35 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 35 pptx

... numerical solutions of differential equations. In researches,especially after the advent of computer, the numerical solutions of the differential equations havebecome easy for manipulations. Hence, ... (Proved)PROBLEM SET 6. 21. Use Trapezoidal rule to evaluate 130xdx∫ consisting five sub-intervals. [Ans. 0. 26] 2. Calculate an approximate value of integral /20sinxdxπ∫, by using Trapezoidal rule.[Ans. ... = 0 .69 315452. Ans. 6. 10 EULER-MACLAURIN’S FORMULAThis formula is based on the expansion of operators. Suppose () (),Fx fx∆= then an operator 1−∆,called inverse operator, is defined as...
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A textbook of Computer Based Numerical and Statiscal Techniques part 40 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 40 pptx

... sensitiveto small changes in A and B i.e., small change in A or B causes a large change in the solution of the system. On the other hand if small changes in A and B give small changes in the solution,the ... NUMERICAL AND STATISTICAL TECHNIQUES largest coefficient of y. We continue this process till last equation. This procedure is known aspartial pivoting. In general, the rearrangement of equation ... approximations: 1.075,x = 2.524y = and 2. 765 z = correct to three decimals. Ans.8 .6. 2 Guass-Seidel MethodThis is a modification of Gauss-Jacobi method. As before, the system of the linear equations....
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A textbook of Computer Based Numerical and Statiscal Techniques part 41 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 41 pptx

... taking suitable scale when the value of x are given at equally spaced intervals.Let h be the width of the interval at which the values of x are given and let the origin of x and y be taken ... a x b x=+∑∑∑ (5)The equation ()3 and ()4 are known as normal equations.On solving equations ()3 and ()4, we get the value of a and b. Putting the value of a and b in equation ... best values for a and b using the observedvalues of v and p. Thus the general problem is to find a suitable relation or law that may existbetween the variables x and y from a given set of...
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A textbook of Computer Based Numerical and Statiscal Techniques part 46 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 46 pptx

... the type and nature of the variations in the data.2. The segregation and study of the various components is of paramount importance to a businessman in the planning of future operations and in ... 1 = 64 .41978 2 58 + 3.4 × 2 = 64 .8Example 8. Fit a straight-line trend equation by the method of least square and estimate the trendvalue.Year 1 961 1 962 1 963 1 964 1 965 1 966 1 967 1 968 Values ... BASED NUMERICAL AND STATISTICAL TECHNIQUES If quarterly data are given, first find quarterly totals for each quarter and the averagesfor the four-quarter of the years. To find these averages,...
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A textbook of Computer Based Numerical and Statiscal Techniques part 50 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 50 pptx

... 0.147=4 76 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Sol. Mean ChartMean of 10 sample mean 44244.210 10xX ===∑Mean Range of 10 sample ranges 585.810 10RR ===∑As we have, ... removed.478 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES whether there are any assignable causes. If assignable causes found, the process should bere-adjusted to remove assignable cause.2052042032022012001991981971 96 195Sample ... cause.2052042032022012001991981971 96 195Sample Mean0 2 4 6 8 10 12Sample NumberMean ChartFIG. 11.19Range Chart108 6 420Sample Range0 5 10 15Sample NumberFIG. 11.20Example 3. In a glass factory, the task of quality...
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A textbook of Computer Based Numerical and Statiscal Techniques part 58 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 58 pptx

... i);break;}}}return 0;}ArraysThe declarationint i;declares a single variable, named i, of type int. It is also possible to declare an array of severalelements. 564 COMPUTER BASED NUMERICAL ... ewhere v is any vairable (or anything like a[ i]), op is any of the binary arithmetic operators, and e is any expression.558 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES printf("can’t compute ... performance.Function BasicsIt has a name that you call it by, and a list of zero or more arguments or parameters that you handto it for it to act on or to direct its work; it has a body containing the actual...
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