numerical analysis 3. 135 points/ The following data have been recorded for a function f(a). 2 3 (2.4142 2.6734 2.8974 3.0976 3.2804 r5 Use Romberg's method to approximate f f(r)dr by completi...
Suppose that f() is a non-negative and continuous function on the interval [a,b]. The following method (illustrated in the below figure) is a well-known method to approximate the total area underneath the curve of f(x) on the given interval: • Divide the interval [a, b] into 3 subintervals cach of width • For each 1 <is 3, choose any arbitrary point in the ith subinterval. • Thus, the total area underneath the curve of f(x) can be approximated by: 3...
Consider the following function. f(x) = 5 sinh (3r). a = 0, n=5,-0.3<r <0.3 (a) Approximate f by a Taylor polynomial with degree n at the number a. 3 45x 2 81 5 T5(x) = | 15x + + -X 8 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f = 7,(x) when x lies in the given interval. (Round the answer to four decimal places.) |R5(x)] = 5.19674 X
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...
question b please Consider the following function f(x) -x6/7, a-1, n-3, 0.7 sx 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a 343 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ,(x) when x lies in the given interval. (Round your answer to eight decimal places.) IR3(x)0.00031049 (c) Check your result in part (b) by graphing Rn(x)l 2 1.3 0.00015 0 0.9 1.0 11 -0.00005 0.00010 -0.00010 0.00005 0.00015 0.8...
13 points SCalcET8 11 11,015 Consider the following function. f(x)-x57, a 1, n-3, 0.7Sxs 1.3 (a) Approximate fby a Taylor polynomial with degree n at the number a. T3(x) (b) Use Taylo's Inequality to estimate the accuracy of the a pproximation Rx)· (x) when x lies in the given interval. (Round your answer to eight de IR2(x)I s (c) Check your result in part (b) by graphing IR,(). 0.00015 1.3 0 0.9 1.0 1.1 -0.0000S 0.00010 -0.0001o 0.00005 -0,00015 8...
help wanted?? thank you explain correctly Problem 1 Use the trapezoidal rule technique to approximate the following integrals: a) 「(x2+1)dr(Note: use 0.5 increments forx) b) sina d INote: use a MATLAB function to subdivide the interval into eight equal parts) c e dx (Note: use 0.25 increments for x Problem 2 Use the Simpson's rule to evaluate the following integrals aDdr Problem 3: Given the polynomial: x3-6x2 + 30-0, Use MATLAB to find all roots of this polynomial. Use MATLAB's...