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.] ( x y ) 2 + x y − x = 8 , ( − 8 , 0 )
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.] ( x y ) 2 + x y − x = 8 , ( − 8 , 0 )
Solution Summary: The author calculates the slope of tangent line to the graph of the equation (xy)2+x-x=8 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.]
(
x
y
)
2
+
x
y
−
x
=
8
,
(
−
8
,
0
)
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.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
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
Chapter 4 Solutions
Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th
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