Homework Answers

<e> Solve using the method of separation of variables the pde partial du/dt+du/dx+2e^tu=0

<e> A vending treasury is purchased for RM 2,800 in cash with RM 700 down payment and fourteen monthly payments. If the interest calculated is 10% per annum, using the fixed rate equation calculation find:

1. Total interest charged

2.Secondly. monthly payment

<e> Let f

f be a function such that at each point (x,y)

(x,y) on the graph of f

f, the slope is given by dy

dx

=1

2

x−1

4

y

2

dydx=12x−14y2. The graph of f

f passes through the point (1,−2)

(1,−2) and is concave up on the interval 1<x<1.5

1<x<1.5. Let k

k be the approximation for f(1.3)

f(1.3) found by using the locally linear approximation of f

f at x=1

x=1. Which of the following statements about k

k is true?

<e> Examine the f:R->R defined by

f(x)={1/6(x+1)^3 x is not equal to 0

5/6 x=0}

for continuity on R .If it is not continuous at any of R find the nature of discontinuity there

<e> m is a straight line with a 1 on the right side.

n is a straight line with a number 3 & 2 in the middle but there’s a diagonal line that goes straight through both lines and the numbers 3 & 2 are in between that diagonal line.

Given: Line m is parallel to line n.

Prove: <1 is supplementary to <3

statement: reason:

S1. Line m is parallel to line n. R1. given

S2. <1 =~ <2 R2. ?

S3. m<1 =~ m<2. R3. ?

S4. <2 & <3 for a linear pair. R4. definition of linear pair

S5. <2 is supplementary to <3 R5. ?

S6. m<2 + m<3 = 180° R6. definition of supplementary

S7. ? R7. Substitution Property of Equality

S8. ? R8. Definition of supplementary

<e> Solve the first order linear inhomogeneous differential equation using the constant variation method

y^,- (3y/x)=x

[DMe] Define group. Show that the set P3 of all permutations on three symbols 1,2,3 is a finite non-abelian group of order six with respect to permutation multiplication as composition.