At the end of this course, each student should be able to: Define the concepts of functions, range, and domain at the conclusion of this session, Use maps to diagrammatically depict the link between Range and Domain.
List the various types of functions.
Limits and continuity.
Differentiation is...
2
dy 1 4 sec x
3
dx y x tan x
2
dy 4 sec x
x e tan x{ 3
4 3x
}
dx x tan x
,3. y x sin 2 x cos 4 x
5
ln y ln x ln sin 2 x ln cos 4 x
5
dy 1 1 1 1
5 .5 x
4
2 cos 2 x . 4sin
dx y x sin 2 x cos 4 x
dy 1 1 1
y{ 5 .5 x
4
2 cos 2 x . 4si
dx x sin 2 x cos 4 x
dy 5
x sin 2 x cos 4 x{ 2 cot 2 x 4 tan 4 x}
5
dx x
, Implicit function
If y=𝒙𝟐 − 𝟒𝒙 + 𝟐, 𝒚 is completely defined in terms of x
y is called an explicit function of x.
When the relationship between x and y is more involve
may not be possible(or desirable) to separate y compl
on the LHS , e.g. xy+siny =2. In such a case as this
called an implicit function of x, because a relation
of the form y=f(x) is implied in the given equation.
it may still be necessary to determine the derivat
of y with respect to x and in fact this is not at all
, All we have to remember is that y is a functio
x, even if it is difficult to see what it is. I
fact, this is really an extension of our ‘funct
of a function’ routine.
𝑥 2 +𝑦 2 =25, as it stands is an example of an
implicit function.
Once again, all we have to remember is that y i
2 2 𝑑𝑦
function of x. so, if 𝑥 +𝑦 =25, let us find
21-Jun-20 MTH 121- General Mathematics II (Calculus)
𝑑
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