Numericalanalysisandcomputationexam - Word File Home Insert Design Layout References Mailings Review View Tell me what you want to do.. & Share Cut Times New Rc - 12 - A" A Aa - |A|:= - 1= - 8 7 . . 3 21 1 AaBbCcDd AaBbCcDd AaBbCc AaBbCct Aa B Find AaBbCCD AaBbCcDd AaBbCcDd AaBbCcDd AaBbCcDc AaBbCcDd Copy Fac Replace Paste 1 Normal 1 No Spac... Heading 1 Heading 2 Title Format Painter BI U - abe X2 X A Z . A . = = 1 2. Subtitle Subtle Em... Emphasis Intense E... Strong Quote Select - Clipboard Font Paragraph Styles Editing Qn.1 1. Suppose we measure the length of a table to be X. = 59.7 inches, but the true value is Xa =59.5 inches. Find a) Error b) Absolute error CAVENDISH c) Relative error (Show all the working and formulas required) (5 marks @) 2. The width of a rectangular piece of land is measured to be 48. 25ft, if the measurement has a relative error of Er of at most 2%, then what is an upper bound for the absolute error? (5 marks) 3. Suppose the ambient temperature is A = 76.20 + 0.40F. In what interval does the true temperature lie? (5 marks) (Total 25 marks) On.2 a) Use Taylor's theorem to expand sin (" + h) in ascending powers of h as far as the term in h+ (10 marks) b) Find the Taylor's polynomial Po. P1. P2 and Ps for f(x) = In(x) at x =1 Use a graphing utility to compare the graph of f (x) with graphs of Po. P1. P2 and p3 (15 marks) Cavendish University Uganda - Examinations, 2022 Page 1 of 2 Page 1 of 2 412 words & English (United States) 85 -- + 120% HOLDCE x ] N XI ENG 10:57 PM UK 26/05/2022 1Numericalanalysisandcomputationexam - Word File Home Insert Design Layout References Mailings Review View Tell me what you want to do.. & Share Cut Times New Rc - 12 - A" A Aa - |A = - 1= - 2 7 . | 2 21 1 Find AaBbCCD AaBbCcDd AaBbCcDd AaBbCcDd AaBbCcDc AaBbCcDd Copy AaBbCcDd AaBbCcDd AaBbCc AaBbCct Aa B Fac Replace Paste Format Painter BI U - abe X2 X' A- Z A .= = = = 1 2. 1 Normal 1 No Spac... Heading 1 Heading 2 Title Subtitle Subtle Em... Emphasis Intense E... Strong Quote Select Clipboard Font Paragraph Styles Editing On. 3 a) Develop a series for sinh x using Maclaurin's series. (15 marks) b) Produce a power series for cos 2x as far as the term in x (10 marks) Qn.4 Use the Maclaurin's series a) Expand ex in ascending powers of x as far as the term x'. (5marks) b) Show that when x is small, sinx ~ x -2+ (15 marks) c) Find the first three terms of the expansion of cos x in ascending powers of x (5 marks) Qn.5 a) Find the Maclaurin series for tan-1(x2), use any terms of your choice. (10 marks) b) Use the first two non-zero terms of an appropriate series to give an approximation of So sin(x2) dx (15 marks) ACU On.6 Derive the following series AVENDISH Page 2 of 2 412 words X English (United States) 50 -- + 120% Ed w ] N XI ENG 10:58 PM UK 26/05/2022 1Numericalanalysisandcomputationexam - Word File Home Insert Design Layout References Mailings Review View Tell me what you want to do.. & Share Cut Times New Rc - 12 - A" A Aa - |4 := - 1= - 2 7 - 2 2 21 1 AaBbCcDd AaBbCcDd AaBbCc AaBbCct Aa B Find Copy AaBbCCD AaBbCcDd AaBbCcDd AaBbCcDd AaBbCcDc AaBbCcDd Fac Replace Paste Format Painter BIU - abe X2 X? A - Z . A . = = = 1 2 . 1 Normal 1 No Spac... Heading 1 Heading 2 Title Subtitle Subtle Em... Emphasis Intense E... Strong Quote Select Clipboard Font Paragraph Styles Editing b) Use the first two non-zero terms of an appropriate series to give an approximation of So sin(x2) dx (15 marks) CU Qn.6 Derive the following series CAVENDISH a) f(x) = f(0) +f'(0)x1 +24! 2! 3! 4! 2x2+0 3+f0 4+f2x5+.......... 5 ! (10 marks) b) f (x) = f(a) +!@(x-a)+ 2 + (" (@( x-a)2+"(@(x ( x - a) 3+ !(@(x 4 ! ( x - a ) 4 (15 marks) Couandich Univercity Llaanda - Examinatione 20)2 Dogo 1 of 2 Page 2 of 2 412 words X English (United States) 8 5 -- + 120% HOLDCHOP Ed w] N XI ENG 10:58 PM UK 26/05/2022 1