Graphs of Inverse Functions Have Reciprocal Slopes In Exercises 13-16, show that the slopes or the graphs of f and f − 1 are reciprocals at the given points. Function Point f ( x ) = x 3 ( 1 2 , 1 8 ) f − 1 ( x ) = x 3 ( 1 8 , 1 2 )
Graphs of Inverse Functions Have Reciprocal Slopes In Exercises 13-16, show that the slopes or the graphs of f and f − 1 are reciprocals at the given points. Function Point f ( x ) = x 3 ( 1 2 , 1 8 ) f − 1 ( x ) = x 3 ( 1 8 , 1 2 )
Solution Summary: The author proves that the slopes of the graphs are reciprocals at the given points.
Graphs of Inverse Functions Have Reciprocal Slopes In Exercises 13-16, show that the slopes or the graphs of f and
f
−
1
are reciprocals at the given points.
1.
(i)
(ii)
which are not.
What does it mean to say that a set ECR2 is closed?
[1 Mark]
Identify which of the following subsets of R2 are closed and
(a)
A = [-1, 1] × (1, 3)
(b)
B = [-1, 1] x {1,3}
(c)
C = {(1/n², 1/n2) ER2 | n EN}
Provide a sketch and a brief explanation to each of your answers.
[6 Marks]
(iii) Give an example of a closed set which does not have interior
points.
[3 Marks]
A company specializing in lubrication products for vintage motors produce two
blended oils, Smaza and Nefkov. They make a profit of K5,000.00 per litre of
Smaza and K4,000.00 per litre of Nefkov. A litre of Smaza requires 0.4 litres of
heavy oil and 0.6 litres of light oil. A litre of Nefkov requires 0.8 litres of heavy oil
and 0.2 litres of light oil. The company has 100 litres of heavy oil and 80 litres of
light oil. How many litres of each product should they make to maximize profits
and what level of profit will they obtain? Show all your workings.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
Chapter 3 Solutions
Calculus: Early Transcendental Functions (MindTap Course List)
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