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Limits
Limits
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One-sided limits graphically
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38 cards
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Questions
38
Answers
1
Algebraic Limits
2
1
1/2
1/4
2
Calculate the Definite Integral.
7/3
14/3
-14/3
-7/3
3
lim x →2
-
1
0
-1
DNE
4
Algebraic Limits
DNE
2
1
0
5
lim x →4
0
DNE
-1
-2
6
Derivatives
cos(e-x) + e-x
cos(e-x) - e-x
-e-x cos(e-x)
-cos(e-x)
7
Take the first derivative of the function y=x
5/2
+3x+4
(5/2)x3/2 +3
(5/2)x3/2
(10/4)x6/4 + (6/3)
(3/2)x5/2 +3
8
Find the derivatives
9x+ 3
3x+3
3x^2 + 6
6x+3
9
Using the product and chain rule find dy/dx of y = x
4
[5x+3]
3
Factor and simplify.
4x3(5x+3)2[15x4(5x+3)
x4(5x+3)2 [35x+12]
60x4(5x+3)5
x3(5x+3)2 [35x+12]
10
lim x→-1
0
1
DNE
-1
11
For which value does a limit exist?
-1
0
1
2
12
Calculate the definite integral.
12
-6
16
24
13
The zeros of the first derivative are the ? of the original function
zeros
Points of Inflection
xintercepts
critical points
14
Find the equation of the tangent line at x=4 of x
2
+4x+6.
y-12=4(x-38)
y-38=12(x-4)
y-38=4(x-4)
y-4=12(x-38)
15
A derivative is a very specific calculus term which, in business applications means...
All of the above.
depreciation or growth
marginal (cost, profit, revenue, etc...)
rate of change
16
Graphic Limits
I only
II and III
III only
II only
17
Find the indefinite integral of...
x2 - x3
x3 + c
x3 - x2
x2 - x3 + c
18
Point of inflection justification?
f ' changes from inc to dec or dec to inc
f '' changes sign
f '' changes from inc to dec or dec to inc
f ' changes sign
19
At which value of x does f(x) = lim f(x) ?
-1
-3
2
none
20
Find the equation of a line tangent to the point (3, 31) on the curve y = 3x
2
+4.
y-31=9(x-3)
y-31=18(x-3)
y-4=18(x-31)
y-4=9(x-31)
21
f(1) =
-1
2
DNE
0
22
Calculate the definite integral.
15
1/15
-1/15
-15
23
lim x→1
+
DNE
0
-1
2
24
INTEGRATION
A
C
B
D
25
Find the indefinite integral of...
2x + C
X2/2+7x
X2/2+7x+C
7x2 + C
26
INTEGRATION
D
B
A
C
27
What rule would you use to evaluate this derivative?
NO RUNNING IN THE HALLS
Product Rule [f(x)g'(x) + g(x)f'(x)]
Chain Rule [n (f(x))n-1 * f'(x)]
Quotient Rule (LoDiHi-HiDiLo / LoLo)
28
lim x → -1
-
1
DNE
2
-1
29
f(2) =
DNE
1
-1
0
30
Tabular Limits
Option 1
DNE or 0
Option 2
Option 4
31
What is the definite integral?
The full area above the curve
The area above the curve between two points
The full area below the curve
The area under the curve between two points
32
What is the derivative of y=ln(3x
5
)
dy/dx = 5/x
dy/dx = 5/x^5
dy/dx = 1/3x^5
dy/dx = 1/ln(3x^5)
33
Given f(x)=x
4
(5x-2)
3
f'(x) requires product AND chain rule.
False
True
34
Find the first derivative of the following function:
20(18x2)4
20(6x3)4
4(6x3)5 × (18x2)
20(6x3)4 × (18x2)
35
Derivatives
2
-2
4
0
36
What is the derivative of y=e
x^2+4
dy/dx = 2x e2x
dy/dx = e2x
dy/dx = 2x ex^2+4
dy/dx = (x2+4)ex^2+4
37
What is the limit as x → 3
1
-1
DNE
0
38
This is the average value theorem for an integral (FB#4)
False
True
