Assignment 1 b

Assignment 1 b

• 1.
  INDERPRASTHA ENGINEERING COLLEGE,GHAZIABAD Tutorials/ Assignments/ Quizzes Subject Name ENGINEERING MATHEMATICS-III Subject Code NAS-301 Date of Handout 21/8/2015 Max Marks Date of Submission 24/8/2015 Q1 Prove that (a) (i) ∆ ∇ - ∇ ∆ = ∆ + ∇ (ii) ߜଶ E = ∆ଶ (iii) ߤߜ = ∆ା ∇ ଶ = ∆ ଶ + ∆ ଶ ‫ܧ‬ିଵ (b) Find the missing term of following table X 10 15 20 25 30 35 F(x) 43 ? 29 32 ? 77 Q2. (a) Use Newton Gregory formula to find the polynomial of degree 3 .Hence find y (3.5) From following table: x 3 4 5 6 y(x) 6 24 60 120 (b) Find the number of men getting wages between Rs/- 10 and Rs/-15 from following table Wages(Rs/-) 0 - 10 10 - 20 20 - 30 30 - 40 Frequency 9 30 35 42 (c) From following table calculate y(12) by Newton forward and backward interpolation Formula and explain why difference occur in result (if any) X 10 15 20 25 30 35 F(x) 35.3 32.4 29.2 26.1 23.2 20.5 Q3 (a) Use Lagrange’s formula to find f(6) and also find value of x for which f(x) is maximum or minimum from the data f(1) = 4 , f (2) = 5, f (7) = 5 ,f(8) = 4 (b) Use Newton divided difference formula to form the function y = f(x) in powers of (x-1) given that f(0)=8 ,f(1) = 11 ,f(4) = 68, f(5) = 123.Also find f(2),f″(2). Answers 1(b) F(15) = 33.933, F(30)= 46.733 2(a) x3 – 3 x2 + 2 x , y(3.5) = 13.125 2(b) 15 2(c) 34.22007,34.30866 3(a) f(6) = 5.66 , x= 4.5 3(b) f(x)=x3 – x2 + 3 x + 8 = (x-1)3 + 2(x-1)2 +4(x-1) + 11 ,f(2)=18, f″(2)=10