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Practice: Linear Approximation (1)
Related Topics
Wize University Calculus 2 Textbook > Multivariable Functions
Tangent plane & Linear Approximation
4 Activities
Find the linear approximation to
z
=
3
+
x
2
25
+
y
2
49
at
(
1
,
1
)
z=3+\frac{x^2}{25}+\frac{y^2}{49}~\text{at}~(1,~1)
z
=
3
+
25
x
2
+
49
y
2
at
(
1
,
1
)
.
Type in the rest of the equation
L
(
1
,
1
)
=
L(1,1)=
L
(
1
,
1
)
=
I don't know
Check Submission
More Tangent plane & Linear Approximation Questions:
Gradient and Directional Derivative
Use linear approximation to estimate the value of function
f
(
x
,
y
)
=
x
2
e
x
y
f(x,y)=x^2e^{xy}
f
(
x
,
y
)
=
x
2
e
x
y
at point (1.01, 1.01).
Practice: Tangent Planes, Gradient Vectors, Normal Lines (1)
An ant is crawling along a flat concrete surface with the temperature of the surface at a point (x, y) given by
T
=
x
3
e
4
x
2
+
y
3
T=x^3e^{4x^2+y^3}
T
=
x
3
e
4
x
2
+
y
3
.
a) At (3, -1), what is the direction of the greatest decrease of the temperature?
b) Find the rate of change of the temperature if the ant crawled from (3, -1) at speed 1 in the direction of the vector
<
10
,
−
4
>
.
<10,~-4>.
<
10
,
−
4
>
.