2.8 Linear Apporsimaations and vitterentials
Jef. The linearization or linear approximation of f at x=c
is LEAS= at cas (x-a)
Turgoat Line
Big Iden: x(x) for & "near" a
Example:
us a
linearization to approximate sin (0.17
[Find tangent line (limerization) of fass="nos) at x=_0
Point: (0, sincos) ={(0,0)
Slope: f'(0) = cos(0) = 1
y=0+ | (x-6)_ Linarlzation
4(x)=x <
(Dig
Dig Idea: sincszex for x "new" 0.
7
f' and frecasy to compute at
this venue
Sin (al) 20.1
Calculator: sin(01) = 0.0999274166...
.
overestimate
y=4&5
2.5-
Q: How could
We use
a
lineurization to
A: Find linearization of x √x at x=9
(1.3) 445=3+=(x-9) 3-1-(85-9)
(9,3
approx
58.5
Jx
忝
amatinale
((8.5T) Z44)
34
74½(-5)
3-12=33
fifl fi fi
Jef. The linearization or linear approximation of f at x=c
is LEAS= at cas (x-a)
Turgoat Line
Big Iden: x(x) for & "near" a
Example:
us a
linearization to approximate sin (0.17
[Find tangent line (limerization) of fass="nos) at x=_0
Point: (0, sincos) ={(0,0)
Slope: f'(0) = cos(0) = 1
y=0+ | (x-6)_ Linarlzation
4(x)=x <
(Dig
Dig Idea: sincszex for x "new" 0.
7
f' and frecasy to compute at
this venue
Sin (al) 20.1
Calculator: sin(01) = 0.0999274166...
.
overestimate
y=4&5
2.5-
Q: How could
We use
a
lineurization to
A: Find linearization of x √x at x=9
(1.3) 445=3+=(x-9) 3-1-(85-9)
(9,3
approx
58.5
Jx
忝
amatinale
((8.5T) Z44)
34
74½(-5)
3-12=33
fifl fi fi
