assinment maths

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