Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Calculus > Limits > Flashcards

Limits Flashcards

1
Q

Explain limits

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Standard limits 1

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Standard limits 2

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Standard limits 3

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Standard limits 4

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Standard limits 5

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Standard limits 6

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Standard limits 7

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Standard limits 8

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Standard limits 9

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Standard limits 10

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Indeterminate forms (7)

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

L-Hospital Rule

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

If you have limit approaches to infinity and polynomial, what to do?

A

Take the highest degree common

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

If you have 0x∞ form, what to to

A

If you have 0x∞ form, make it in 0/0 or ∞/∞ form
example: f(x).g(x) is in the 0x∞ form then write it as

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

If you ∞-∞ indeterminate form, what to do

A

Write function into another form
for ex: make unrationalized into rationalized

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

If x->0 then (1+x)ⁿ

A

If x->0 then (1+x)ⁿ ≅1+nx

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

When will (1+x)ⁿ becomes 1+nx

A

when x->0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Piecewise function

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

How to break |f(x)|

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

What is f(x) = |x|

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What is f(x) = |cos x|

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What to do in mode graph

A

Make the -ve y graph (i.e. graph in 3rd and 4th quadrant) +ve (i.e. make the mirror image w.r.t. to x axis of -ve)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Greatest integer function

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

How to pronounce greatest integer function

A

Floor of x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Another name of gif

A

Step function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

Notation of gif

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

Explain gif
(Short)

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

Explain continuity of gif

A

Discontinuous function at every integer

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

continuity of f(x)

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

if limit doesn’t exit then

A

it means f(x) at x=a doesn’t follow LHL = RHL = f(a)
and graph is discontinuous at x=a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

Leibnitz rule

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

What is the differentiation of an integration with variable limits

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

Derivative of a function f at any point x

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

Differentiability of f(x) at x=a

A
36
Q

Derivative by first principle

A
37
Q

Explain relation between continuity and differentiability of f(x)

A

Every differentiable function is continuous but every continuous function need not be differentiable
For ex: f(x) = |x|

38
Q

How to tell that function is differentiable or not (if graph is given)

A
39
Q

Even function

A

f(-x) = f(x) ∀ x∈R

40
Q

Odd function

A

f(-x) = -f(x) ∀ x∈R

41
Q

Graph of even function

A

symmetric about y-axis

42
Q

Graph of odd function

A

symmetric about origin

43
Q

Differentiation of even function

A

is odd function

44
Q

Differentiation of odd function

A

even function

45
Q

Another name of derivative

A

gradient

46
Q

Explain Partial differentiation

A
47
Q

Total derivative of z

A
48
Q

Partial derivative of z w.r.t x

A
49
Q

Partial derivative of z w.r.t y

A
50
Q

What is this (see pic)

A
51
Q

What is this (see pic)

A
52
Q

dz/dx

A
53
Q

dz/dy

A
54
Q

dz/dy

A
55
Q

What is this(see pic)

A
56
Q

What is this(see pic)

A
57
Q

another notation of this (see pic)

A
58
Q

another notation of this (see pic)

A
59
Q

What is this

A
60
Q

What is this

A
61
Q

What is this

A
62
Q

Homogeneous function

A

u = f(x,y) is a homogeneous function of degree ‘n’ iff f(kx,ky) = kⁿf(x,y)

63
Q

Shortcut of homogeneous function

A

Degree of every term is same

64
Q

special point about homogeneous function

A

if you have rational function, both numerator and denominator are homogeneous then function is also homogeneous

65
Q

degree of homogeneous function

A

degree(numerator) - degree(denominator)

66
Q
A
67
Q
A
68
Q
A
69
Q
A
70
Q
A
71
Q

Euler theorem types

A

Type 1: u = f(x,y) is a homogenous function of degree n
Type 2: u = f(x,y) + g(x,y) where f, g are homogeneous functions of degree n₁ and degree n₂ respectively
Type 3: Φ(u) = f(x,y) is a homogeneous function of degree ‘n’

72
Q

Euler theorem type 1

A

Type 1: u = f(x,y) is a homogenous function of degree n then
i.) xuₓ + yuᵧ = nu
ii.) x²uₓₓ + y²uᵧᵧ + 2xyuₓᵧ = n(n-1)u

73
Q

Euler theorem type 2

A

Type 2: u = f(x,y) + g(x,y) where f, g are homogeneous functions of degree n₁ and degree n₂ respectively then
i.) xuₓ + yuᵧ = n₁f + n₂g
ii.) x²uₓₓ + y²uᵧᵧ + 2xyuₓᵧ = n₁(n₁-1)f + n₂(n₂-1)g

74
Q

Euler theorem type 3

A

Type 3: Φ(u) = f(x,y) is a homogeneous function of degree ‘n’ then
i.) xuₓ + yuᵧ = nΦ(u)/Φ’(u) = F(u)
ii.) x²uₓₓ + y²uᵧᵧ + 2xyuₓᵧ = F(u) [F’(u) - 1]

75
Q

What to do in this type of function where we need to apply homogeneous function concept

A
76
Q

What is the relationship between
dy/dx and dx/dy ?

A

Both are reciprocals of each other

77
Q

Chain rule

A
78
Q

Mean value theorems (3)

A

1.) Roll’s theorem
2.) Lagrange’s mean value theorem
3.) Cauchy’s mean value theorem

79
Q

Rolle’s theorem (brief)

A
80
Q

Explain Rolle’s theorem

A
81
Q

What does f’(c) = 0 means if function satisfying the Rolle’s theorem

A

If once the function is satisfying the Rolle’s theorem, there exist at least one point where the function can reach its peak values like minimum values or maximum values.

82
Q

Lagrange’s mean value theorem (brief)

A
83
Q

Explain Lagrange’s mean value theorem

A
84
Q

What does f’(c) gives in Lagrange’s mean value theorem and what it doesn’t give

A

Using Lagrange’s mean value theorem, f’(c) gives derivative of f(c) at certain point b/w (a,b)
f’(c) doesn’t gives maxima or minima since f’(c) is not zero

85
Q

Cauchy’s mean value theorem

A

Calculus (7 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions