問題一覧
1
If y = f(x) is any function, then g(y) or y = f^-1 (x) is its inverse function.
Inverse Function
2
It occurs when no general limit exists at the given x value.
Jump Discontinuity
3
It is set of appropriate input that a function accepts.
Domain
4
Determine the rate
0.4 m/s
5
Find the derivative
(b/a) cos t
6
Find the c
2 ± 1/√3
7
Find the k
11
8
Find the angle
71.57°
9
Find Ro at temperature of 0°C
25 Ohm
10
Find the slope
-3
11
Find the allowable error
0.0025 m
12
If y = f(x) is a function, where y = f(-x) = f(x)
Even Function
13
Find f(100)
458
14
Find 99th derivative
-cos x
15
Evaluate the limit
No Limit
16
Find the slope
3/2
17
Find the slope
-1.73
18
Infinite Discontinuity is also referred as _____.
Essential Discontinuity
19
A manufacturer has 600 liters of a 12% solution of acid. How many liters of 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18?
Between 120 L and 300 L
20
If y = f(x) is a function, where y = f(-x) = -f(x)
Odd Function
21
Point Discontinuity is also referred as _____
Removable Discontinuity
22
Find the 2nd derivative at x = 2
0.375
23
Find the equation
5x + 4y - 41 = 0
24
It is an iteration method for solving the zero of a function where f is assumed to have continuous derivative f, Xn+1 = Xn - f(Xn)/f'(Xn).
Newton's Method
25
Evaluate the limit
e
26
It is specific kind of relation such that every input has only one matching output
Function
27
Find the slope
3
28
Find the velocity when accelaration is zero
0.33 m/s
29
Find the slope
-4.94
30
Find the value of a
2
31
Find derivative
x^x(1 + ln x)dx
32
Find the domain
x²/9 + y²/1 > 1
33
How fast is the third side increasing
0.201 m/s
34
Find y^(50)
50!
35
Find the rate
0.64 m/s
36
Consider the function: f(x) = x³/9 - 3x. At what interval will the function increasing?
(-infinity, -3) and (3, infinity)
37
Definition
Function
38
Find the c
Ln(e - 1)
39
How fast is surface area
2 cm²/min
40
Find y'
sec^2 (x)
41
Find the first derivative
4x^3
42
Find the velocity
35.60 ft/s
43
A collection of related numbers or ordered pairs
Relation
44
Given a function f(x) = Ax² + Bx + C, When x = 3, f(x) = -12, x = 2, f(x) = -15 and minimized at x = 1. Find C.
-15
45
It occurs when a general limit exists but function value is not defined at that particular x value.
Point Discontinuity
46
Find the equation
2x + 3y - 6 = 0
47
Find the linear approximation
33x - 150
48
It occurs when no general limit exists at the given x value.
Jump Discontinuity
49
Evaluate the limit
3
50
If y = f(x) is a function, where y = f(x + nT) = f(x)
Periodic Function
51
It occurs when no general limit exists at the given x value.
Jump Discontinuity
52
Oil spilling from a ruptured tanker spread in a circle on the surface of the ocean. The area of the spill increases at a rate of 9π m²/min. How fast is radius of spill increasing when radius us 10 m?
9/20 m/min
53
It occurs when the function does not have limit and it is not defined at that particular x value.
Infinite Discontinuity
54
Definition
Extreme Value Theorem
55
What is first derivative dy/dx
-y(1 + ln xy)/x
56
Find the points
(1.125, 4.5)
57
Find the equation
2.6x - y - 3.85 = 0
58
Definition
Rolle's Theorem
59
Given a function f(x) = Ax² + Bx + C, When x = 3, f(x) = -12, x = 2, f(x) = -15 and minimized at x = 1. Find A.
1
60
Find the critical points
(-2, -14)&(2, 18)
61
Find the rate
-8
62
The value of f(x) is 12 when x = 6. If f(x) ≤ 10, what is f(x) when x = 15?
102
63
Find the slope
2/5
64
Water leaking unto a floor forms a circular pool. The radius of pool increases at rate of 4 cm/min. How fast is the area of pool increasing when radius is 5 cm.
40π cm²/min
65
Find the inflection points
(1, 7)
66
Given a function f(x) = Ax² + Bx + C, When x = 3, f(x) = -12, x = 2, f(x) = -15 and minimized at x = 1. Find B.
-2
67
Find dy/dx
1/(y² + 1)
68
Find the angle
70.53°
69
Find the partial derivative
2xy³z⁴
70
Find the rate
140π cm^3
71
Definition
Mean Value Theorem
72
Find the minimum value
12
73
Definition
Cauchy Mean Value Theorem
74
Points that are the highest or lowest of all the local extrema in graph.
Absolute Extrema
75
Definition
Identity
76
Find the second derivative
-2a²x²/y⁵
77
A maximum or minimum point occurs when point is lower or higher than all points.
Relative Extrema
78
Find the linear approximation
L(x) = (3 - x)e^(-2)
79
Find the derivarive
-2
80
Evaluate the limit
1/3
81
Find the f(-3)
-262
82
How fast is lower end moves
15 m/min
83
Find the allowable error
4.71 mm³
84
Find the value of Sqrt(20+Sqrt(20+Sqrt(20+.......)))
5