In a group of 25 students, 15 are enrolled in Lab, 8 are enrolled in EconTwo, and 5 are neither enrolled in Lab nor EconTwo. How many are enrolled in at least one of the subjects? How many are enrolled in Lab 1. alone, and in EconTwo alone? 2. Evaluate the limit: lim Vx – 12 x→12 3. Solve for m s.t. the function is continuous (Do not use L'Hospital's Rule and Do not use shortcuts) x2 – 9 f(x) = } x + -3 x + 3 т+2 x = -3 4. Given the function, g(x) 3 x < 0 (2х — g(x) = 0 2 a. Determine the possible points of discontinuity. b. Discuss the continuity/discontinuity of the function at the points determined in (a). dy given: dx 5. Determine ax*y3 – bxy = 36 where a and b are constants. 6. Verify Young's Theorem x2 z = In(2x + y) · + e(x+2y) + y
In a group of 25 students, 15 are enrolled in Lab, 8 are enrolled in EconTwo, and 5 are neither enrolled in Lab nor EconTwo. How many are enrolled in at least one of the subjects? How many are enrolled in Lab 1. alone, and in EconTwo alone? 2. Evaluate the limit: lim Vx – 12 x→12 3. Solve for m s.t. the function is continuous (Do not use L'Hospital's Rule and Do not use shortcuts) x2 – 9 f(x) = } x + -3 x + 3 т+2 x = -3 4. Given the function, g(x) 3 x < 0 (2х — g(x) = 0 2 a. Determine the possible points of discontinuity. b. Discuss the continuity/discontinuity of the function at the points determined in (a). dy given: dx 5. Determine ax*y3 – bxy = 36 where a and b are constants. 6. Verify Young's Theorem x2 z = In(2x + y) · + e(x+2y) + y
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:In a group of 25 students, 15 are enrolled in Lab, 8 are enrolled in
EconTwo, and 5 are neither enrolled in Lab nor EconTwo. How many are
enrolled in at least one of the subjects? How many are enrolled in Lab
1.
alone, and in EconTwo alone?
2.
Evaluate the limit:
lim Vx – 12
x→12
3. Solve for m s.t. the function is continuous (Do not use L'Hospital's Rule and Do not use shortcuts)
x2 – 9
f(x) = }
x + -3
x + 3
т+2
x = -3
4.
Given the function, g(x)
3
x < 0
(2х —
g(x) =
0 <x< 2
x > 2
a. Determine the possible points of discontinuity.
b. Discuss the continuity/discontinuity of the function at the points determined in (a).
dy
given:
dx
5.
Determine
ax*y3 – bxy = 36
where a and b are constants.
6.
Verify Young's Theorem
x2
+–+e(x+2y)
y
z = In(2x + y)
7.
| Evaluate the following limit using L'Hospital's Rule, when applicable:
2m?
+
Зт? + 1
16т + 4
lim
V9m + 3
m-00
8.
z = f(x,y) = 2y³ – xy + 2x² , where y = 3m x = 6m + 3
a. Find the total differential of z
b. Find the dz/dm
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