Engineering Mathematics: Solved Problems and Examples

ENGINEERING MATHEMATICS
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Q1. What is the period of sinusoidal function y=4sin (-2x+7)-1
Answer: The period is determined using the formula 2 π
¿ b∨¿¿ , replacing b with -2 in the period
formula
Period= 2 π
¿−2∨¿ ¿, solving the equation
The absolute value is determined by the distance between zero and a number thus the distance
between -2 and 0 is 2
The common factor will cancel out 2 π
2 . Diving π by 1, we get π
The period of the sinusoidal wave is thus π
Q2. Consider an aeroplane is pointing towards South and flying with an airspeed of 120 m/s.
Simultaneously there is a steady wind blowing due West with a constant speed of 40 m/s.
a) Make a sketch that shows how to find the resultant velocity of the plane
cos θ= 40
126.49

θ=71.56 °
tanθ= 120
40 , θ=251.56 ° whichis the direction angle
b) What is the resultant speed of the aeroplane?
126.49 m/s
Q3.1. If f(x) =x3-9x, what is the average rate of change of f over the interval [1, 6]?
The average rate of change of a function is established by evaluating the change in the
values of y of the two pointes and then dividing the resultant by the change in the values of x of
the two points
f ( 0 ) −f (6)
( 0 )−(1)
Substituting the equation y=x3-9x for f (0) and f (6) and substituting the x in the function with the
corresponding values of x
{1 ¿ ¿=-8/-1=8
Q3.2 If f(x) =ln (x)/, find the rate of change of f(x) between 1 and 1.5
Answer: The average rate of change is determined by
f ( 1.5 ) −f (1)
1.5−1 = ln ( 1.5 ) −ln(1)
0.5 = ln(0.5)
0.5 =−1.38629
Q3.3. What is the rate of change of the interval π ≤ x ≤ 4 π /3, for the function y=4 sin x-7
f ( 4 π /3 )−f (π)
( 0 )−(1) = 0.969−2.624
1.047 =−1.581