# MAT135H1 Lecture Notes - Lecture 1: Differential Calculus

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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 point ‘P’? (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