ChE 4117L
Exercise 1
Instruction: Solve the following problems using Mathcad. Show clearly the flow of your solutions and write it on a short bond paper.
1.
Evaluate each of the following.
a.
lim
x 2
x3  x2  4
x2  4
d.
 /2
tan 2
b. lim
  0 2 sin 2 
c.
dx
 x(2  3x)
e.
 2 sin
3
 cos 2  d
g.
y  x 2  3 find dy/dx when x = 2
h. y 
0
d
((sec x  tan x) 1 )
dx
f.
d 3
( x sin x  x 2 cos x)
dx
i.
1 2
( x  3 x) 3 find y’, y’’ and y’’’
x
d (cot 2 ) 2
dx 1   2
2.
3.
Find the three consecutive odd numbers of which 4/7 of the sum of the first and second equals the third number decreased by one.
From the top of a building 60 ft high, the angle of elevation of the top of a vertical pole is 14 o. At the bottom of the building the angle of
elevation of the top of the pole is 28o. Find (a) the height of the pole and (b) the distance of the pole from the building.
4.
5.
6.
Solve log 4
 log 7 for x.
Points A and B are on opposite sides of a lake. At a point C, which is 456 feet from A and 580 feet from B, the angle subtended by the lane
AB is 44o 35’. Find the distance from A to B.
Find two numbers whose sum is 10, and the sum of whose squares is a minimum.
7.
Expand
8.
Invert the following transforms:
x 3
x 1
2
by partial fraction expansion.
( s  1)( s  1) 2 ( s  3)
2
3s
1
b.
2
2
( s  1)( s  4)
s ( s  2s  5)
s 1
2s
9. Obtain y(t) for 2
and
.
s  2s  5
( s  1) 3
1
10. Invert the function y ( s )  2
and plot y(t) versus t.
( s  1) 2
11. Plot sin  , cos  and tan  in one graph. (Note: -2 < y < 2 and -10 < x < 10 for ordinate and abscissa respectively.)
a.
2
ChE 4117L
Exercise 1
Instruction: Solve the following problems using Mathcad. Show clearly the flow of your solutions and write it on a short bond paper.
1.
Evaluate each of the following.
a.
lim
x 2
x3  x2  4
x2  4
d.
dx
 x(2  3x)
 /2
tan 2
b. lim
  0 2 sin 2 
e.
d
((sec x  tan x) 1 )
c.
dx
d 3
( x sin x  x 2 cos x)
f.
dx
 2 sin
3
 cos 2  d
0
g.
y  x 2  3 find dy/dx when x = 2
h. y 
1 2
( x  3 x) 3 find y’, y’’ and y’’’
x
d (cot 2 ) 2
i.
dx 1   2
2.
3.
Find the three consecutive odd numbers of which 4/7 of the sum of the first and second equals the third number decreased by one.
From the top of a building 60 ft high, the angle of elevation of the top of a vertical pole is 14o. At the bottom of the building the angle of
elevation of the top of the pole is 28o. Find (a) the height of the pole and (b) the distance of the pole from the building.
4.
5.
6.
Solve log 4
 log 7 for x.
Points A and B are on opposite sides of a lake. At a point C, which is 456 feet from A and 580 feet from B, the angle subtended by the lane
AB is 44o 35’. Find the distance from A to B.
Find two numbers whose sum is 10, and the sum of whose squares is a minimum.
7.
Expand
8.
Invert the following transforms:
x 3
x 1
2
by partial fraction expansion.
( s  1)( s  1) 2 ( s  3)
2
3s
1
b.
2
2
( s  1)( s  4)
s ( s  2s  5)
s 1
2s
9. Obtain y(t) for 2
and
.
s  2s  5
( s  1) 3
1
10. Invert the function y ( s )  2
and plot y(t) versus t.
( s  1) 2
11. Plot sin  , cos  and tan  in one graph. (Note: -2 < y < 2 and -10 < x < 10 for ordinate and abscissa respectively.)
a.
2