Section 1
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∫ sec x dx?
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Last updated
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Date created
Mar 1, 2020
Cards (138)
Section 1
(50 cards)
∫ sec x dx?
ln |sec x + tan x| + c is the integral of what?
∫ tanh(x) dx
ln(cosh(x)) + C Is the integral for what?
∫ sinh(x) dx
cosh(x) + C Is the integral for what?
∫ tan x dx?
-ln |cos x| + c is the integral of what?
∫ a^x dx?
a^x/ ln a + c is the integral of what?
∫ sech(x) dx
sin⁻¹ (tanh(x)) + C Is the integral for what?
∫ csc x dx?
-ln |csc x + cot x| + c is the integral of what?
∫ ln x dx?
x ln x - x + c is the integral of what?
Formula for integrating using the washer method?
is the formula for what?
sin²x + cos² x=?
1
∫ dx/(a² + x²)?
1/a arctan (x/a) + c is the integral of what?
d/dx (ln x)?
1/x is the derivative of what?
∫ sin x dx?
-cos x + c is the integral of what?
1 + cot² x=?
csc² x
∫ dx/(sqrt(a² - x²))?
arcsin (x/a) + c is the integral of what?
∫ a dx?
ax + c is the integral of what?
∫ cot x dx?
ln |sin x| + c is the integral of what?
d/dx (sin x)?
cos x is the derivative of what?
Formula for integrating using the disk method?
is the formula for what?
d/dx (sec x)?
sec x tan x is the derivative of what?
Arc Length Formula?
Is the integral for what?
∫ csc² x dx?
- cot x + c is the integral of what?
∫ csch(x) dx
ln |tanh(x/2)| + C Is the integral for what?
d/dx arctan (x) ?
is the derivative of what?
∫ tan² x dx?
tan x - x + c is the integral of what?
d/dx (csc x)?
-csc x cot x is the derivative of what?
∫ cosh(x) dx
sinh(x) + C Is the integral for what?
∫ coth(x) dx
ln |sinh(x)| + C Is the integral for what?
d/dx (cot x)?
- csc² x is the derivative of what?
What is the formula for Hooke's Law?
Hooke's Law: F=kd is force (f) equals the spring constant (k) times the distance (d).
d/dx (arcsec x)?
is the derivative of what?
∫ 1/x dx?
ln | x | + c is the integral of what?
Formula for integrating about the line x=0 using the shells method?
Is the formula for what?
What is the area of a circle geometrically?
π(a²) a=radius is the area of what?
What is the formula for integrating about the line y=0 using the shell method?
Is the formula for what?
1 + tan² x=?
sec²(x)
∫ cos x dx?
sin x + c is the integral of what?
d/dx (a^x)?
is the derivative of what?
∫ sec² x dx?
tan x + c is the integral of what?
d/dx arcsin (x) ?
is the derivative of what?
d/dx (tan x)?
sec² x is the derivative of what?
d/dx (cos x)?
- sin x is the derivative of what?
∫ csc x cot x dx?
- csc x + c is the integral of what?
∫ e^x dx?
e^x + c is the integral of what?
∫ sec x tan x dx?
sec x + c is the integral of what?
sin(-x)=?
-sin x -sin(x) = sin(-x) or only -sin(x)?
d/dx (e^x)?
is the derivative of what?
Section 2
(50 cards)
Definition of Continuity
1. lim x→c f(x) exists. 2. f(c) exists. 3. lim x→c f(x) = f(c)
cos(pi/3)=?
1/2 is the arccos of what?
tan(pi/3)=?
sqrt(3) What is the arctan of the sqrt of (3)?
d/dx arccsc(x)?
Is the derivative for what?
What is the formula for csch(x)?
Is the formula for what function?
tan(0)=?
0 what is the arctan of 0?
Integral of 1/sqrt(a^2+x^2) dx
arcsinh of (x/a) + C Is the integral for what?
integral of 1/sqrt(a^2-x^2) dx
arcsin of (x/a) + C Is the integral for what?
d/dx arccos(x)?
Is the derivative for what?
sin(pi/4)=?
sqrt of 2 divided by 2 is the arcsin of what?
Quotient Rule
d/dx (g(x)/ h(x)) = (h(x) g'(x) - g(x) h'(x))/ h(x)^2
sin(0)=?
0 is the arcsin of what?
Surface Area of a Sphere?
where a is a constant Is the formula for what?
sin(pi/3)=?
sqrt of 3 divided by 2 is the arcsin of what?
cos(pi/4)=?
the sqrt of 2 divided by 2 is the arccos of what?
The formula for the arcsech?
is the formula for what?
What is the formula for cosh(x)?
Is the formula for what function?
Product Rule
d/dx (f(x) g(x)) = f(x)g'(x) + g(x) f'(x)
tan(pi/2)=?
undefined in the first quadrant where is the arctan undefined?
Surface Area Formula?
Is the integral for what?
What is the formula for the Moment about Y? (COM or centroid of a lamina)
d/dx arccot(x)?
Is the derivative for what?
sin(pi/2)=?
1 is the arcsin of what?
sin(pi/6)=?
1/2 is the arcsin of what?
cos(pi/6)=?
the sqrt of 3 divided by 1/2 is the arccos of what?
Definition of a Derivative
lim h→0 (f(x+h) - f(x)) / h
The formula for arccosh(x)?
Is the formula for what?
Formula for sinh(x)?
Is the formula for what function?
The formula for the arccsch?
is the formula for what?
What is the C.O.M. formula for M(mass)? (COM or centroid of a lamina)
Integral of 1/sqrt(x^2-a^2) dx
arccosh (x/a) + C Is the integral for what?
When does the limit not exist?
1. f(x) approaches a different number from the right as it does from the left as x→c 2. f(x) increases or decreases without bound as x→c 3. f(x) oscillates between two fixed values as x→c
What is the formula for tanh(x)?
Is the formula for what function?
cos(0)=?
1 is the arccos of what?
The formula for arcsinh? (x)?
is the formula for what?
Integral of 1/a^2+x^2 dx
1/a arctan (x/a) + C Is the integral for what?
The formula for arctanh?
is the formula for what?
cos(pi/2)=?
0 is the arccos of what?
What is the formula for sech(x)?
Is the formula for what function?
What is the formula for the Moment about X? (COM or centroid of a lamina)?
The formula for the arccoth?
is the formula for what?
d/dx arcsec(x)?
Is the derivative for what?
d/dx arccsc(x)?
Is the derivative for what?
tan(pi/4)=?
1 What is the arctan of 1?
What is the formula for a collection of masses along a straight line?
Is the formula for what?
Integral of 1/(a^2-x^2) dx
1/a arctanh (x/a) + C Is the integral for what?
Intermediate Value Theorem
If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b) then there is at least one number c in [a, b] such that f(c) = k
What is the shorthand for x-bar and y-bar? (COM)
tan(pi/6)=?
the sqrt of 3 divided by 3 what is the arctan of sqrt(3)/3?
What is the formula for coth(x)?
Is the formula for what function?
Section 3
(38 cards)