University | Singapore University of Social Science (SUSS) |
Subject | Engineering Mathematics |
Engineering Mathematics 2 Assignment Questions
Question 1.
(A). Determine whether the following series is convergent or divergent by applying the relevant tests:
(i). 5+10+15+20+25+30+35+…+…
(ii). ∑_(n=0)^∞=〖(-1)〗^n
(B). Evaluate the limit of the following sequence
(i). {(〖4n〗^2+5n+7)/(〖-8n〗^2+6n+5)}_(n=0)^(+∞)
(ii). {(n^2+7n)/(〖2n〗^3-12)}_(n=0)^(+∞)
(iii). {√((3n+2)/(12n-7))}_(n=0)^(+∞)
(C). Use the limit comparison test to determine whether the series , ∑_(n=0)^∞=1/√(n^2-9)is convergent or divergent.
Question 2.
(A). Find the centre, radius and interval of convergent for following power series: ∑_(n=0)^∞=1/(1+n^3 ) 〖(x+3)〗^n
(B). Find the radius and interval of convergent of power series ∑_(n=0)^∞=〖n(x+3)〗^n/4^(n+1)
(C). Find the Maclaurin series for e^x
(D). Find the first four terms of Taylor series for cosx at x=3
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Question 3
(A). Find ∂y/∂x and ∂z/∂x for x^4+y^4+z^4+x^2 y^2 z^2=0
(B). Find the Jacobian (∂(x,y))⁄(∂(u,v))
(i). x=2u+3v,y=u-3v
(ii). x=7u+v,y=2u+5v
(C). Suppose f(x,y,z)=x^3 y^2+xz+2z=3;
Given: x=2 sint;
y=2cost;
z=1;
(i). Find df/dt
(ii). Evaluate df/dt when t=0 for f (1,1,1)
Question 4
(A). Find the critical points of the following function, then determine whether they are the relative maximum, relative minimum or saddle points
f(x,y)=〖2x〗^3-〖27x〗^2+48x+〖2y〗^3-18y^2+48y+222
(B). Find the divergence and curl of the following vector fields:
(i). F(x,y,z)= xyzi+2y^2 zj+〖3z〗^2 k
(ii). F(x,y,z)= z sin y i+4xz j- cos 9z k
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