(b) Given the function f(x) = x2 (x-2)(x-3)2 i. Decompose f(x) into partial fractions (6 marks,...
x2-x+6 x3 +3x 7./Use the Apart command to decompose i into partial fractions. Question: which case is this?? Now find the antiderivative of each fractional expression by hand. Note: you will need to split apar of your fractions even further. You may use any of the shortcuts mentioned in Appendix G work below. t one . Show all x2-x+6 x3 +3x -11xs+914-222xx+39x+2 dx 8. Find the antiderivative: 3x6 -11x5 +9x4 -2x3 -x2 +9x -7 Make use of the Apart command,...
use partial fractions to find the integral 16. x2 - x + 9 J (x2 + 9)2 dx
4. Consider the following partial information about a function f(x): S.x2, 0<x<I, (2-x), 1<x<2. Given that the function can be extended and modelled as a Fourier cosine-series: (a) Sketch this extended function in the interval that satisfies: x <4 (b) State the minimum period of this extended function. (C) The general Fourier series is defined as follows: [1 marks] [1 marks] F(x) = 4 + ] Ancos ("E") + ] B, sin("E") [1 marks] State the value of L. (d)...
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)
C. Involving Partial fractions 4 z+ 2z + 3 S x2 + 5x – 14 dx in S2-6)(22+4) dz 4x - 11 dx iv) *342 + 4)(22 +7) 8 +t+6t2 - 12t3 dt.
calculus 2 (please show all work so i can understand ) 9. Given f(x) = (x-5)/(x2 - x-2) find a geometric power series for f(x). Hint: partial fractions.
5. (6 marks) Rewrite the following expressions using partial fractions. Check your results using Matlab. (a) s + 2 /s(s + 1) (b) s + 1 /(s − 1)2 (c) s 2 + 1 /s 2 − 1 5. (6 marks) Rewrite the following expressions using partial fractions. Check your results using Matlab. 3 +2 3+ 1 $2+1 (a) 38 +1) (b) is - 1) (c) 52 - 1
Decompose 4+2 -2x2 + 5x + 3 into partial fractions, showing all of your work. You may either enter your solution using the equation editor in the space provided or submit your written work to the
(a) Resolve the expansion 2 ac (x - 1)(x + 2) into partial fractions sums. (b) Hence determine the binomial expansion up to and including the term involving x?.
(a) Given the following function f(x) below. Sketch the graph of the following function A1. f () 3 1, 12 5 marks (b) Verify from the graph that the interval endpoints at zo and zi have opposite signs. Use the bisection method to estimate the root (to 4 decimal places) of the equation 5 marks] (c) Use the secant method to estimate the root (to 4 decimal places) of the equation 6 marks that lies between the endpoints given. (Perform...