Classify each statement as either true or false. Match each function in column A with the most appropriate rule to use for differentiating the function. [ 1 . 5 , 1 . 6 ] For f ' ( 5 ) to exists, f must be continuous at 5 . [ 1 . 4 ]
Classify each statement as either true or false. Match each function in column A with the most appropriate rule to use for differentiating the function. [ 1 . 5 , 1 . 6 ] For f ' ( 5 ) to exists, f must be continuous at 5 . [ 1 . 4 ]
Solution Summary: The author explains that if a function is differentiable at x=a, then it is continuous. Differentiability implies continuity at that point.
Match each function in column A with the most appropriate rule to use for differentiating the function.
[
1
.
5
,
1
.
6
]
For
f
'
(
5
)
to exists, f must be continuous at
5
.
[
1
.
4
]
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.
Electric charge is distributed over the triangular region D shown below so that the charge density at (x, y)
is σ(x, y) = 4xy, measured in coulumbs per square meter (C/m²). Find the total charge on D. Round
your answer to four decimal places.
1
U
5
4
3
2
1
1
2
5
7
coulumbs
Let E be the region bounded cone z = √√/6 - (x² + y²) and the sphere z = x² + y² + z² . Provide an
answer accurate to at least 4 significant digits. Find the volume of E.
Triple Integral
Spherical Coordinates
Cutout of sphere is for visual purposes
0.8-
0.6
z
04
0.2-
0-
-0.4
-0.2
04
0
0.2
0.2
x
-0.2
04 -0.4
Note: The graph is an example. The scale and equation parameters may not be the same for your
particular problem. Round your answer to 4 decimal places.
Hint: Solve the cone equation for phi.
* Oops - try again.
The temperature at a point (x,y,z) of a solid E bounded by the coordinate planes and the plane
9.x+y+z = 1 is T(x, y, z) = (xy + 8z +20) degrees Celcius. Find the average temperature over
the solid. (Answer to 4 decimal places).
Average Value of a function
using 3 variables
z
1-
y
Hint: y = -a·x+1
* Oops - try again.
x
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY