Study sets matching "calculus 1"

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Study sets matching "calculus 1"

48 terms
Calculus 1
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
Calculus 1
Function
Domain
Range
Vertical Line Test
An equation, in a table, by a graph, or in words
Independent variable
Dependent variable
Determines if a curve in the xy-plane is the graph of a funct…
Function
An equation, in a table, by a graph, or in words
Domain
Independent variable
Calculus 1
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 1
Difference Quotient
Piecewise functions
Logarithmic Function
Trigonometric Functions
Function expressed by two or more different formulas over dif…
and/or A^y = X
Sine X ... Cos X ... Tan X ... Sec X ... CSC X ... CoTan X
Difference Quotient
Piecewise functions
Function expressed by two or more different formulas over dif…
14 terms
Calculus - Set #1
-sinx
cosx
sec²x
-cscxcotx
-sinx
cosx
9 terms
AP Calculus 1- Limits
End behavior
Exponential Decay
Exponential Growth
Limit
The appearance of a graph as it is followed farther and farth…
A model for decay of a quantity for which the rate of decay i…
This model is used for such phenomena as inflation or populat…
The value that a function or expression approaches as the dom…
End behavior
The appearance of a graph as it is followed farther and farth…
Exponential Decay
A model for decay of a quantity for which the rate of decay i…
27 terms
Calculus 1
Function
Domain
x²x³
x²/x³
Assigns to each number in its domain another number... Takes 1…
Consists of all numbers for which the rule makes sense. All n…
x²⁺³
x²⁻³
Function
Assigns to each number in its domain another number... Takes 1…
Domain
Consists of all numbers for which the rule makes sense. All n…
13 terms
Calculus 1
cosx
-sinx
sec2x
secxtanx
d/dx sinx
d/dx cosx
d/dx tanx
d/dx secx
cosx
d/dx sinx
-sinx
d/dx cosx
Calculus 1!
Metacognition ( Five things to remembe…
Five Step Problem Solving process (alg…
Function
Write Equations of Parallel and Perpen…
1. Assess the task—Get a handle on what is involved in comple…
1. Familiarize yourself with the problem... 2. Identify the kno…
a function from a set X to a set Y is a rule for assigning to…
Metacognition ( Five things to remembe…
1. Assess the task—Get a handle on what is involved in comple…
Five Step Problem Solving process (alg…
1. Familiarize yourself with the problem... 2. Identify the kno…
Calculus 1
Point-slope form
Sin(x) is odd/even ?
Cos(x) is odd/even?
Trig Function relating to Pythagorean…
Y-b = m ( X-a )
odd, sin(-x)=-sin(x)
Even, cos(-x)= cos(x)
(sin(x))^2 + (cos(x))^2 = 1
Point-slope form
Y-b = m ( X-a )
Sin(x) is odd/even ?
odd, sin(-x)=-sin(x)
12 terms
Calculus 1
d/dx (sinx)
d/dx(cosx)
d/dx(tanx)
d/dx(cscx)
cosx
-sinx
sec^2(x)
-cscxcotx
d/dx (sinx)
cosx
d/dx(cosx)
-sinx
38 terms
Calculus 1
d/dx(sinx)
d/dx(cosx)
d/dx(tanx)
d/dx(cscx)
cosx
-sinx
sec²x
-cscxcotx
d/dx(sinx)
cosx
d/dx(cosx)
-sinx
14 terms
calculus 1
Limit Does NOT Exist when:
Formal Definition of Limit:
Squeeze Theorem
Continuous at point x=c
1. f(x) approaches different number from L and R... 2. Vertical…
if a fuc is between two other functions, both having a limit…
Limit Does NOT Exist when:
1. f(x) approaches different number from L and R... 2. Vertical…
Formal Definition of Limit:
Calculus 1
Foundation 1: I can state 2 things tha…
Foundation 2: I can state 2 things tha…
Foundation 3
D1:
1.) The instantaneous rate of change and 2.) the slope of the…
1.) the net change; 2.) the area between a curve and the x-axis
I can estimate derivatives numerically
I can state what limits informally mean
Foundation 1: I can state 2 things tha…
1.) The instantaneous rate of change and 2.) the slope of the…
Foundation 2: I can state 2 things tha…
1.) the net change; 2.) the area between a curve and the x-axis
43 terms
Calculus 1
lim [c•f(x)]
lim [f(x)+g(x)]
lim [f(x)-g(x)]
lim [f(x)•g(x)]
c•lim f(x)
lim f(x)+lim g(x)
lim f(x)-lim g(x)
lim f(x)•lim g(x)
lim [c•f(x)]
c•lim f(x)
lim [f(x)+g(x)]
lim f(x)+lim g(x)
17 terms
Calculus 1
Completing statements with meaning of…
Completing statements with meaning of…
If f(x) is continuous at x = r then li…
The expression that defines the deriva…
"we can keep the numbers produced by f(x)=____ as close as we…
"we can keep the numbers produced by (whatever is beside limi…
f(r)
Completing statements with meaning of…
"we can keep the numbers produced by f(x)=____ as close as we…
Completing statements with meaning of…
"we can keep the numbers produced by (whatever is beside limi…
56 terms
Calculus 1
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 1
Non Differentiable functions
Derivative
Integration
Fractional Exponents
undefined slope or vertical tangent line.
Slope of a curve... (slope= "rate" of change)
"Fancy term" for addition ... Adding "area" under a curve into s…
Roots
Non Differentiable functions
undefined slope or vertical tangent line.
Derivative
Slope of a curve... (slope= "rate" of change)
Calculus - Limits Day 1
Evaluate the limit ... Lim (x-2)/(x²-4)…
Evaluate the limit ... Lim (x+2)/((√x²-4…
Evaluate the limit ... Lim (x²-1)/(x+2)…
Evaluate the limit ... Lim (x²-4)/(x-2)…
1/4
dne
3/4
4
Evaluate the limit ... Lim (x-2)/(x²-4)…
1/4
Evaluate the limit ... Lim (x+2)/((√x²-4…
dne
11 terms
Calculus 1
L'hospital's Rule
Integration by parts
The reciprocal rule
linear approximation
Integral uv' dv = uv - integral v u' dx
L'hospital's Rule
Integration by parts
Integral uv' dv = uv - integral v u' dx
Calculus 1
dy/dx arccos(x)
dy/dx tan(x)
dy/dx arcsin(x)
dy/dx a^x
a^x × ln(a)
dy/dx arccos(x)
dy/dx tan(x)
75 terms
Calculus 1
cos(2x)
sec²(x)
csc²(x)
cscx prime
cos²(x)-sin²(x)... 2cos²(x)-1... 1-2sin²(x)
1+tan²(x)
1+cot²(x)
-cotxcscx
cos(2x)
cos²(x)-sin²(x)... 2cos²(x)-1... 1-2sin²(x)
sec²(x)
1+tan²(x)
24 terms
Calculus, Lesson 1
natural numbers (N)
counting numbers
positive integers
whole numbers
numbers that we naturally use to count
numbers that we naturally use to count
numbers that we naturally use to count
numbers that we naturally use to count, including 0
natural numbers (N)
numbers that we naturally use to count
counting numbers
numbers that we naturally use to count
Calculus 1
Lim x→ 0, sinx/x =
Lim x→ ∞, sinx/x =
Defined is
Exists is
1
0
the point @y
arrows leading up to y
Lim x→ 0, sinx/x =
1
Lim x→ ∞, sinx/x =
0
calculus 1
derivative rules
constant rule
derivative of x
power rule
derivative of a constant... derivative of x... power rule... constant…
derivative of a constant is 0
is x
move the exponent around subtract one from current exponent
derivative rules
derivative of a constant... derivative of x... power rule... constant…
constant rule
derivative of a constant is 0
8 terms
Calculus 1
Sin(x)/x=
Cos (x) -1/x
Sin ' (x)
Cos ' (x)
1
0
Cos x
-sin (x)
Sin(x)/x=
1
Cos (x) -1/x
0
6 terms
Calculus 1
Function
1-1 function
Invertible function
Functions that have inverses
A function f having domain set A and range(codomain) set B is…
F:A----->B is a 1-1 function if it is a function which satisf…
A function f:A----->B, where b has been chosen to consist pre…
Theorem: if f is a 1-1then it is invertible. If f is invertib…
Function
A function f having domain set A and range(codomain) set B is…
1-1 function
F:A----->B is a 1-1 function if it is a function which satisf…
Calculus 1
Point-slope form
Sin(x) is odd/even ?
Cos(x) is odd/even?
Trig Function relating to Pythagorean…
Y-b = m ( X-a )
odd, sin(-x)=-sin(x)
Even, cos(-x)= cos(x)
(sin(x))^2 + (cos(x))^2 = 1
Point-slope form
Y-b = m ( X-a )
Sin(x) is odd/even ?
odd, sin(-x)=-sin(x)
Calculus 1
Average Velocity Equation
Secant Line
Instantaneous Velocity
Instantaneous Velocity equation
msec= (s(t1) - s(t0)) / (t1 - t0)
any line joining two points on a curve
The instantaneous velocity is called the limit
(limit,t->1) ((s(t) - s(t1)) / (t - 1))
Average Velocity Equation
msec= (s(t1) - s(t0)) / (t1 - t0)
Secant Line
any line joining two points on a curve
48 terms
Calculus 1
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
Calculus 1
Division by zero is
A function is well defined when
Definition of the absolute value of a…
Definition of principle and truth
UNDEFINED
we get exactly one correct answer
abs(th)={th IF th is greater than or equal to zero... {-th IF t…
nroot(th)^n is equal to th. (You get what's inside when raise…
Division by zero is
UNDEFINED
A function is well defined when
we get exactly one correct answer
43 terms
Calculus 1
f(x)+c
f(x+c)
cf(x)
f(cx)
c: shift up, -c: shift down
c: shift left, -c: shift right
c>1: vertical stretch, 0<c<1: vertical shrink
c>1: Horizontal shrink, 0<c<1: Horizontal stretch
f(x)+c
c: shift up, -c: shift down
f(x+c)
c: shift left, -c: shift right
Calculus 1
d/dx=
sin x
cos x
tan x
nx^n-1
cos x
-sin x
sec^2 x
d/dx=
nx^n-1
sin x
cos x
29 terms
Calculus Semester 1 Review
Squeeze Theorem
f is continuous at x=c if...
Intermediate Value Theorem
nx^(n-1)
If f is continuous on [a,b] and k is a number between f(a) an…
Squeeze Theorem
f is continuous at x=c if...
22 terms
Calculus 1
Even
Odd
Sin^2 x + cos^2 x=
Sin2x=
Reflected over y axis... [f(-x)=f(x)]
Reflected over origin... [f(-x)=-f(x)]
1
2sinxcosx
Even
Reflected over y axis... [f(-x)=f(x)]
Odd
Reflected over origin... [f(-x)=-f(x)]
16 terms
Calculus 1
D/dxsin^-1(x)
D/dx cos^-1(x)
D/dx tan ^1(x)
D/dxsec^1(x)
1/sqrt(1-x^2)
-1/sqrt(1-x^2)
1/(1+x^2)
1/|x|sqrt(x^2-1)
D/dxsin^-1(x)
1/sqrt(1-x^2)
D/dx cos^-1(x)
-1/sqrt(1-x^2)
Calculus 1
Extreme Value Theorem
Fermat's Theorem
Mean Value Theorem
Rolle's Theorem
If f(x) is continuous on a closed interval [a,b] the f(x) att…
If f(x) has a local maximum or minimum at "c" and f'(c) exist…
If f(x) is continuous on the closed interval [a,b], where a<b…
Let f(x) be a function that satisfies the following three hyp…
Extreme Value Theorem
If f(x) is continuous on a closed interval [a,b] the f(x) att…
Fermat's Theorem
If f(x) has a local maximum or minimum at "c" and f'(c) exist…
32 terms
Calculus 1
Limits
The Power Rule
Product Rule
Definition of the Derivative
...
...
...
...
Limits
...
The Power Rule
...
Calculus 1
function
domain
f(x)
codomain
a rule that assigns to each element 'x' in a set 'D' exactly…
set of all possible inputs for a function f
value of f at x, is read as 'f of x'
set of all possible values of 'f(x)'
function
a rule that assigns to each element 'x' in a set 'D' exactly…
domain
set of all possible inputs for a function f
24 terms
Calculus 1
Average velocity
Absolute value
Direct substitution property (limits)
(If a function (f) is) continuous on.…
Change in position/ change in time
|a| distance between a and 0 on a number line: always positiv…
If (f)is a polynomial or a rational function and (a) is in th…
Continuous at every number in the interval.
Average velocity
Change in position/ change in time
Absolute value
|a| distance between a and 0 on a number line: always positiv…
10 terms
Calculus 1
ratio
rate
even function
f(x) = x⁴ + 5x² + 72
x and y have the same unit of measure
x and y have different units of measure
f(-x) = f(x)... all exponents are even numbers
f(-x) = -x⁴ + -x² + 72... f(-x) = x⁴ + x² + 72... even function
ratio
x and y have the same unit of measure
rate
x and y have different units of measure
25 terms
Calculus 1 Midterm
definition of a derivative
Average Velocity
Speed
instantaneous velocity
derivative at point a:... lim x->a f(x)-f(a)/x-a
velocity at a specific point
definition of a derivative
derivative at point a:... lim x->a f(x)-f(a)/x-a
Average Velocity
9 terms
Calculus 1
Chain Rule: [f(g(x))]
Product Rule: [f(x) x g(x)]
Quotient Rule: [f(x) / g(x)]
d/dx constant
f'(g(x)) * g'(x)
f'(x) g(x) + f(x) g'(x)
g(x) f'(x) - f(x) g'(x)... ------------------------... [g(x)]^2
0
Chain Rule: [f(g(x))]
f'(g(x)) * g'(x)
Product Rule: [f(x) x g(x)]
f'(x) g(x) + f(x) g'(x)
30 terms
Calculus 1
Linear Approximations
Mean Value Theorem
Newton's Method
FTC1
L(x)=f(a)+f'(a)(x-a)
f'(c)=f(b)-f(a)/(b-a)
Xn+1=Xn-(f(Xn)/f'(Xn))
if g(x)=integral from a to x f(t) dt then g'(x)=f(x)
Linear Approximations
L(x)=f(a)+f'(a)(x-a)
Mean Value Theorem
f'(c)=f(b)-f(a)/(b-a)
Calculus 1
integral of tan(x) dx
integral of csc(x) dx
integral of sec(x) dx
integral of cot(x) dx
-ln |cos(x)| + C
-ln |csc(x) + cot(x)| + C
ln |sec(x) + tan(x)| + C
ln |sin(x)| + C
integral of tan(x) dx
-ln |cos(x)| + C
integral of csc(x) dx
-ln |csc(x) + cot(x)| + C
Calculus 1
slope
secant
tangent
velocity
meredekség
metszővonal
érintő
sebesség
slope
meredekség
secant
metszővonal
Calculus 1
The formal definition of a derivative
d/dx [c] (constant rule)
d/dx [ax] (linear rule)
d/dx [axⁿ] (general power rule)
0
a
naxⁿ⁻¹
The formal definition of a derivative
d/dx [c] (constant rule)
0
12 terms
Calculus 1
d/dx(sin^-1x)
d/dx(cos^-1x)
d/dx(tan^-1x)
d/dx(cot^-1x)
(1-x^2)^-1/2
-(1-x^2)^-1/2... For -1<x<1
1/(1+x^2)
-1/(1+x^2)... For negative infinity<x<positive infinity
d/dx(sin^-1x)
(1-x^2)^-1/2
d/dx(cos^-1x)
-(1-x^2)^-1/2... For -1<x<1
15 terms
Calculus 1
Function (n)
Relation (n)
Domain (n)
Value (n)
Fonksiyon
Bağıntı
Tanım kümesi
Değer
Function (n)
Fonksiyon
Relation (n)
Bağıntı
5 terms
Calculus 1
Triangle
Circle-A
Circle circumference
Rectangular box volume
1/2 bh
Pr^2
2 pr
Lwh
Triangle
1/2 bh
Circle-A
Pr^2
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