Brainscape's Knowledge GenomeTM


Top Flashcards (Certified)
All Flashcards

Projects > Calculus > Flashcards

Calculus Flashcards

To understand differentiation and integration more effectively

1
Q

Critical points are points in the curve where the slope is

A

zero

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

All critical points are not Local maxima|Local mininma, but all local maxima and local minima has a critical point why

A

Criticial points can also indicate inflection points

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

What does y = x2 gives as curve

A

A Parabolic Curve

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

What does y = x2 gives as curve

A

Similar to a Asymptode

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

What is Differentiation tells you

A

Slope of a tangent line

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

What does integration used for

A

To find AUC and average rate of change of moving objects

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

What are the ways to find slopes

A

If lines - y = mx+c
if curves - Differentiation (Slope of tangent line)
Slope of Secant line

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

What is a Secant Line

A

Secant Line connects two points in a curve

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

Slope of a Secant Line

A

y2 - y1/ x2 - x1

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

how do we find instantaneous rate of change in terms of calculus

A

Differentiation

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

how do we find instantaneous rate of change in terms of calculus

A

Integration

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

How do we find acceleration in terms of Calculus

A

second derivative of the function

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

What is actually a function

A

A relation between Y value and X value

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

What is the difference between f(x) and F(x)

A

f(x) - differentiation,
F(x) - integration

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

What is the difference between f’(x) and f^-1(x)

A

f’(x) = differentiation
f^-1(x) = Inverse function

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

What is the use of this f^-1(x)

A

gives you the value of x wrt to y

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

What is sine wave

A

Starts at 0, peaks at 90, bottoms at 270 and again peaks at 360

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

What is Cosine Wave

A

Starts at 90 peaks at 0, bottoms at 180 and again peaks at 270

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

f(sinx)

A

cosx

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

f(cosx)

A

-sinx

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

f(tanx)

A

sec2x

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

f(cotx)

A

-cosex^2x

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

f(secx)

A

secx tanx

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

f(cosecx)

A

-cosecx tanx

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
What is Power rule in Differentiation
n^x = nx^n-1
26
What is chain rule
dy/dx(f(g'(x)) = f'(g(x) * g'(x) outside first inside second
27
differentiate f(x) g(x)
f'(x) g(x) +f(x) g'(x)
28
differentiate f(x)/g(x)
f'(x) g(x) +f(x) g'(x)/(g(x))^2
29
differentiate c
0
30
differentiate x
1
31
What is LCD
Multiply the numerator and denominator by a common number so that the denominators match for easy calculations
32
What happens when we have bounds of Secant line infinitely close to each other
This resembles Tangent Line
33
What is the limit x->2 when y = x2 means
it means the the value of x is approaching Ly close to 2 it can be 2.1, 2.001
34
What does Squeeze theorem
if b(x) lies between a(x) and c(x) and differentiation of a(x) and b(x) = d. then c(x) is also zero
35
What are continuous curve and non continuous cutves
Non continuous curve has a break/missing(cannot be drawn in a single hand) Continuous can
36
What are continuous curve and non continuous cutves
Non continuous curve has a break/missing(cannot be drawn in a single hand) Continuous can
37
Give an example for non continuous curves
Jump discontinuity, asymptodes
38
What is an odd function and and even function
Odd function is symmentric across either x axis or y axis even function is symmetric across origin
39
What is an odd function and and even function
Odd function is symmentric across either x axis or y axis even function is symmetric across origin
40
What is domain and bounds
Domains are the highest and lowest values of x-axis and bounds are the highest and lowest values of y axis
41
How do you find concavity of a curve
Second derivative of a function gives the distance from the critical point
42
What does it mean if the second derivative of a function is positive
It means that the curve is upwards
43
What does it mean if the second derivative of a function is negative
The curve is concave down
44
How do you find critical value by Extreme value theorem
According to mean value theorem step 1 take the first derivative of the curve and equate it to zero to find x values step 2 substitute X value and identify y value from the curve step 3 apply the lower and higher bounds to the equation these are the critical points of the curve
45
When is first derivative preferred over second derivative while calculating critical points
If the formula involves fractions taking second derivative leads to complications hence first derivative is used
46
What is jerk
It is the third derivative of velocity or second derivative of acceleration
47
What is Local Maxima and Global Maxima
local maxima is a peak in relavance to the nearer points, global maxima is the maxima of all the peaks in the curve
48
How can We interpret limits which respective to their values
Limits from left = Limit from Right => Then its a asymptode
49
Feauture of Vertical Asymptode
y reaches some number, x reaches towards infinity
50
Feauture of Horizontal Asymptode
x reaches some number, y reaches towards infinity
51
Roles Theorem
If f is continous function f is differentiable on (a,b) f(a) = f(b)
52
Mean Value Theorem
If f is continous function f is differentiable on (a,b) Slope is calculated by y2-y1/x2-x1
53
What is Anti Derivative Called as
Integration
54
What is the Use of Integration
To Area Under the Curve by summing up infinitely small number of distances
55
i=1 -> n ∑ C =
C
56
i=1 -> n ∑ i =
n(n+1)/2
57
i=1 -> n ∑ i^2 =
n(n+1)(2n+1)/6
58
i=1 -> n ∑ i^3 =
n^2(n+1)^2/2
59
What is Riemann Integral
Definite Integral
60
What is Definite Integral
Definite Integral Has the bounds
61
What is INdefinite Integral
Indefinite Integral Has no bounds ∫f(x)dx = F(x) + C
62
How to define Sine, Cos, Tan by trigonometry
Sin = opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse Tan = Opposite/Hypotenuse
63
What is Newtons Law in calculus used For
Newton Law is used to point a point in x axis where y value is zero
64
What is Newtons law of Calculus
x(n+1) = xn - ( f(xn)/f'(xn) )
65
Steps in optimization procedure
Understand the question Identify the optimisation equation and the constraints eqn Now solve the constraints equation to get simpler equation Substitute this into the optmisation equation and optimize it (ie derivative =0) Solve it and substitute to constrain eqn and find both values
66
What is optimization in calculus
Optimization helps us to maximize or minimise a function (Ie, finding local maxima or minima)
67
What is optimization in calculus
Optimization helps us to maximize or minimise a function (Ie, finding local maxima or minima)
68
Integration of rate gives
Accumulation

Projects (5 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions