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