Study sets matching "calculus"

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Study sets matching "calculus"

45 terms
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
75 terms
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
54 terms
Calculus!
limit definition (words)
limit DNE
vertical asymptote
horizontal asymptote
the y-value a function approaches from both sides as x approa…
unbounded, infinite, oscillating behavior or jump in graph
at some point x = a, f(x) → ∞... or there's 0 in the denominator
as x → ∞, f(x) approaches some number
limit definition (words)
the y-value a function approaches from both sides as x approa…
limit DNE
unbounded, infinite, oscillating behavior or jump in graph
92 terms
Calculus
f is continuous at x=c if...
Intermediate Value Theorem
Global Definition of a Derivative
Alternative Definition of a Derivative
If f is continuous on [a,b] and k is a number between f(a) an…
f '(x) is the limit of the following difference quotient as x…
f is continuous at x=c if...
Intermediate Value Theorem
If f is continuous on [a,b] and k is a number between f(a) an…
163 terms
Calculus
1.) F(c) exists... 2.) limit F(x) as x ap…
Yes lim+=lim-=f(c)... No, f'(c) doesn't e…
This is a graph of f'(x). Since f'(C)…
1
f is continuous at x=c if...
Given f(x):... Is f continuous @ C... Is f' continuous @ C
Given f'(x):... Is f continuous @ c?... Is there an inflection poin…
1.) F(c) exists... 2.) limit F(x) as x ap…
f is continuous at x=c if...
Yes lim+=lim-=f(c)... No, f'(c) doesn't e…
Given f(x):... Is f continuous @ C... Is f' continuous @ C
Calculus
f is continuous at x=c if...
Intermediate Value Theorem
Global Definition of a Derivative
Alternative Definition of a Derivative
If f is continuous on [a,b] and k is a number between f(a) an…
f '(x) is the limit of the following difference quotient as x…
f is continuous at x=c if...
Intermediate Value Theorem
If f is continuous on [a,b] and k is a number between f(a) an…
12 terms
CALCULUS
Two Special Trigonometric Limits
Definition of the Derivative of a Func…
Average Velocity or Average rate of Ch…
Properties of the Natural Logarithmic…
limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0
f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx
[f(b) - f(a)] / (b - a)
a. The domain is (0, ∝) and the range is (-∝,∝)... b. ln(1) = 0…
Two Special Trigonometric Limits
limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0
Definition of the Derivative of a Func…
f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx
Calculus
f is continuous at x=c if...
Intermediate Value Theorem
Global Definition of a Derivative
Alternative Definition of a Derivative
If f is continuous on [a,b] and k is a number between f(a) an…
f '(x) is the limit of the following difference quotient as x…
f is continuous at x=c if...
Intermediate Value Theorem
If f is continuous on [a,b] and k is a number between f(a) an…
63 terms
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
75 terms
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
56 terms
calculus
0
f'(x) + g'(x)
cf'(x)
f(x)g'(x) + g(x)f'(x)
derivative of a constant
derivative of the summation of two functions
derivative of a constant times a function
derivative of the multiplaction of two functions
0
derivative of a constant
f'(x) + g'(x)
derivative of the summation of two functions
56 terms
calculus
0
f'(x) + g'(x)
cf'(x)
f(x)g'(x) + g(x)f'(x)
derivative of a constant
derivative of the summation of two functions
derivative of a constant times a function
derivative of the multiplaction of two functions
0
derivative of a constant
f'(x) + g'(x)
derivative of the summation of two functions
54 terms
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
50 terms
Calculus
d/dx [cu]
d/dx [u+v]
d/dx [uv]
d/dx [u/v]
cu'
u'+v'
uv'+vu'
(vu'-uv')/v^2
d/dx [cu]
cu'
d/dx [u+v]
u'+v'
56 terms
calculus
0
f'(x) + g'(x)
cf'(x)
f(x)g'(x) + g(x)f'(x)
derivative of a constant
derivative of the summation of two functions
derivative of a constant times a function
derivative of the multiplaction of two functions
0
derivative of a constant
f'(x) + g'(x)
derivative of the summation of two functions
Calculus
∫sinxdx
∫cosxdx
∫tanxdx
∫secxdx
-cosx + C
sinx + C
-ln|cosx| + C or ln|secx| + C
ln|secx + tan x| +C
∫sinxdx
-cosx + C
∫cosxdx
sinx + C
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
calculus
0
f'(x) + g'(x)
cf'(x)
f(x)g'(x) + g(x)f'(x)
derivative of a constant
derivative of the summation of two functions
derivative of a constant times a function
derivative of the multiplaction of two functions
0
derivative of a constant
f'(x) + g'(x)
derivative of the summation of two functions
75 terms
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
56 terms
calculus
0
f'(x) + g'(x)
cf'(x)
f(x)g'(x) + g(x)f'(x)
derivative of a constant
derivative of the summation of two functions
derivative of a constant times a function
derivative of the multiplaction of two functions
0
derivative of a constant
f'(x) + g'(x)
derivative of the summation of two functions
37 terms
Calculus
Product Rule
Quotient Rule
Adding Derivatives
Subtracting Derivatives
f'(x)g'(x)=g(x)f'(x)+g'(x)*f(x)
f(x)/g(x)=(g(x)f'(x)-g'(x)f(x))/(g(x))^2
(f(x)+g(x))'=f'(x)+g'(x)
(f(x)-g(x))'=f'(x)-g'(x)
Product Rule
f'(x)g'(x)=g(x)f'(x)+g'(x)*f(x)
Quotient Rule
f(x)/g(x)=(g(x)f'(x)-g'(x)f(x))/(g(x))^2
calculus
Calculus
Mathematics
Geometry
Algebra
the mathematical study of change, in the same way that geomet…
the study of topics such as quantity (numbers), structure, sp…
a branch of mathematics concerned with questions of shape, si…
one of the broad parts of mathematics, together with number t…
Calculus
the mathematical study of change, in the same way that geomet…
Mathematics
the study of topics such as quantity (numbers), structure, sp…
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
Calculus
Derivative of arcsin
Derivative of arctan
Derivative of arcsec
Derivative of arccos
Derivative of arcsin
Derivative of arctan
60 terms
Calculus
(f(x+h)-f(x))/h
limit of a function
vertical asymptote
average velocity
instantaneous rate of change
suppose f(x) is defined when x is near A (in an open interval…
limx-->af(x)=+-infinity then A is this
displacement over change in time
(f(x+h)-f(x))/h
instantaneous rate of change
limit of a function
suppose f(x) is defined when x is near A (in an open interval…
60 terms
Calculus
cos
sin
tan
sec
adjacent over hypotenuse
opposite over hypotenuse
opposite over adjacent... sin over cos
1 over cos... hypotenuse over adjacent
cos
adjacent over hypotenuse
sin
opposite over hypotenuse
75 terms
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
75 terms
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
176 terms
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
56 terms
calculus
0
f'(x) + g'(x)
cf'(x)
f(x)g'(x) + g(x)f'(x)
derivative of a constant
derivative of the summation of two functions
derivative of a constant times a function
derivative of the multiplaction of two functions
0
derivative of a constant
f'(x) + g'(x)
derivative of the summation of two functions
23 terms
Calculus
Average Value Theorem
Antiderivative of cos and sin
derivative of sinx
derivative of cosx
cosx
-sinx
Average Value Theorem
Antiderivative of cos and sin
calculus
0
f'(x) + g'(x)
cf'(x)
f(x)g'(x) + g(x)f'(x)
derivative of a constant
derivative of the summation of two functions
derivative of a constant times a function
derivative of the multiplaction of two functions
0
derivative of a constant
f'(x) + g'(x)
derivative of the summation of two functions
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
28 terms
Calculus
Quadratic Formula
Factoring Sum and Difference of Cubes
f(c) is not defined.
lim f(x) ... x->c... does not exist.
Quadratic Formula
Factoring Sum and Difference of Cubes
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
30 terms
Calculus
0
Alternative Definition of a Derivative
nx^(n-1)
1
f '(x) is the limit of the following difference quotient as x…
0
Alternative Definition of a Derivative
f '(x) is the limit of the following difference quotient as x…
25 terms
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
calculus
0
f'(x) + g'(x)
cf'(x)
f(x)g'(x) + g(x)f'(x)
derivative of a constant
derivative of the summation of two functions
derivative of a constant times a function
derivative of the multiplaction of two functions
0
derivative of a constant
f'(x) + g'(x)
derivative of the summation of two functions
Calculus
(f(x+h)-f(x))/h
limit of a function
vertical asymptote
average velocity
instantaneous rate of change
suppose f(x) is defined when x is near A (in an open interval…
limx-->af(x)=+-infinity then A is this
displacement over change in time
(f(x+h)-f(x))/h
instantaneous rate of change
limit of a function
suppose f(x) is defined when x is near A (in an open interval…
Calculus
Definite integral definition
Trapezoid Rule (area approximation)
Simpson's Rule (area approximation)
Fundamental Theorem of Calculus
Definite integral definition
Trapezoid Rule (area approximation)
59 terms
Calculus
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
41 terms
Calculus
odd function
When is the origin the midpoint of any…
even function
parametric equation
symmetric in respect to origin; ... f (-x) = - f (x)... sin (x)
When the function is odd
symmetric over y axis;... f (-x) = f (x)... cos (x)
has a third variable (parameter, often shown as t) to find va…
odd function
symmetric in respect to origin; ... f (-x) = - f (x)... sin (x)
When is the origin the midpoint of any…
When the function is odd
56 terms
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
54 terms
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
CALCULUS
Two Special Trigonometric Limits
Definition of the Derivative of a Func…
Average Velocity or Average rate of Ch…
Guidelines for Implicit Differentiation
limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0
f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx
[f(b) - f(a)] / (b - a)
a. Differentiate both sides of the equation with respect to x…
Two Special Trigonometric Limits
limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0
Definition of the Derivative of a Func…
f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx
33 terms
Calculus
State the Intermediate Value Theorem
State the Chain Rule for Differentiation
What is the integral of ln(x)?
What is the Product Rule?
If the function f(x) is continuous on [a,b], and y is a numbe…
n(f(x))^n-1 * f'(x)
...
[f(x) g'(x)] + [f('x) g(x)]
State the Intermediate Value Theorem
If the function f(x) is continuous on [a,b], and y is a numbe…
State the Chain Rule for Differentiation
n(f(x))^n-1 * f'(x)
33 terms
Calculus
State the Intermediate Value Theorem
State the Chain Rule for Differentiation
What is the integral of ln(x)?
What is the Product Rule?
If the function f(x) is continuous on [a,b], and y is a numbe…
n(f(x))^n-1 * f'(x)
...
[f(x) g'(x)] + [f('x) g(x)]
State the Intermediate Value Theorem
If the function f(x) is continuous on [a,b], and y is a numbe…
State the Chain Rule for Differentiation
n(f(x))^n-1 * f'(x)
Calculus
int(1/sqrt(a^2-u^2))du
int(1/a^2+u^2)du
int(1/u(sqrt(u^2+a^2))du
deriv(sinx)
arcsin(u/a)+C
1/a(arctan(u/a))+C
1/a(arcsec(u/a))+C
cos(x)
int(1/sqrt(a^2-u^2))du
arcsin(u/a)+C
int(1/a^2+u^2)du
1/a(arctan(u/a))+C
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