In Exercises 31–42, use implicit differentiation to find (a) the slope of the tangent line and (b) the equation of the tangent line at the indicated point on the graph. (Round answers to four decimal places as needed.) If only the x-coordinate is given, you must also find the y-coordinate. [ HINT: See Example 2 and 3.] 2 x 2 + x y = 3 y 2 , ( − 1 , − 1 )
In Exercises 31–42, use implicit differentiation to find (a) the slope of the tangent line and (b) the equation of the tangent line at the indicated point on the graph. (Round answers to four decimal places as needed.) If only the x-coordinate is given, you must also find the y-coordinate. [ HINT: See Example 2 and 3.] 2 x 2 + x y = 3 y 2 , ( − 1 , − 1 )
Solution Summary: The author calculates the slope of the tangent line to the graph of (-1,-1) using the implicit differentiation.
In Exercises 31–42, use implicit differentiation to find (a)the slope of the tangent line and(b)the equation of the tangent line at the indicated point on the graph. (Round answers to four decimal places as needed.) If only the x-coordinate is given, you must also find the y-coordinate. [HINT: See Example 2 and 3.]
2
x
2
+
x
y
=
3
y
2
,
(
−
1
,
−
1
)
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
ex
5.
important aspects.
Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all
6
33
Chapter 4 Solutions
Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th
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