MAT135H1 Lecture Notes - Lecture 1: Differential Calculus

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Published on 22 Sep 2020
School
Department
Course
Professor
Intro to Calculus
What is Calculus?
o Two simple geometric problems:
o Given a function
()
yfx
=
,
! The problem of tangents [differential calculus]
What is the slope of the tangent to the graph of the function at a given pointP’? (i.e.
instantaneous rate of change)
! The problem of areas [integral calculus]
What is the area under the graph of a function
()
yfx
=
between
xa
=
and
xb
=
?
[recall from grade 12 Advanced Functions]
o The slope of a tangent to the graph
()
yfx
=
at point
(, ())
Pa f a
is given by:
o To find the slope of a tangent at point
(, ())
Pa f a
! find the value of
()
fa
[i.e. replace x with a]
! find the value of
fa h
+
[i.e. replace x with a+h]
! evaluate 0
()()
limh
fa h fa
h
+
I
mlijnoHath fCa
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