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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
14 terms
Calculus - Set #1
-sinx
cosx
sec²x
-cscxcotx
-sinx
cosx
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
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…
32 terms
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…
90 terms
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…
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
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…
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
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
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
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:
13 terms
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
48 terms
Calculus 1
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
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
22 terms
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)
38 terms
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)
15 terms
Calculus 1
Function (n)
Relation (n)
Domain (n)
Value (n)
Fonksiyon
Bağıntı
Tanım kümesi
Değer
Function (n)
Fonksiyon
Relation (n)
Bağıntı
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
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)
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...
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
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)
33 terms
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
16 terms
Calculus 1
slope
secant
tangent
velocity
meredekség
metszővonal
érintő
sebesség
slope
meredekség
secant
metszővonal
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
26 terms
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
26 terms
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
20 terms
Calculus 1
(u/v)'
(logb(f(x))'
(ln(f(x))'
(b^f(x))'
(u'v-uv')/v^2
(f '(x))/(f(x)(ln(b)))
(f '(x))/(f(x))
(b^f(x))(ln(b))f '(x)
(u/v)'
(u'v-uv')/v^2
(logb(f(x))'
(f '(x))/(f(x)(ln(b)))
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
15 terms
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
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)]
21 terms
Calculus 1
Linearization
Differentials
Mean Value Theorem
Find the domain
L(x) = f(a)+f'(a)(x-a)
dy = f'(x)dx
f'(c) = (f(b)-f(a))/(b-a)
Set the function equal to zero and find where it cannot equal…
Linearization
L(x) = f(a)+f'(a)(x-a)
Differentials
dy = f'(x)dx
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)
22 terms
Calculus 1.
vertical shift
Horizontal shift
vertical stretching and shrinking
horizontal stretching and shrinking
f(x)+c is up... f(x)-c is down
f(x-c) is to the right... f(x+c) is the left
Cf(x) if C is greater than 1 than stretch... if C is less than…
f(Cx) if C is greater than 1 it shrinks... if C is less than 1…
vertical shift
f(x)+c is up... f(x)-c is down
Horizontal shift
f(x-c) is to the right... f(x+c) is the left
50 terms
Calculus 1
underlie
million
seismograph
seismic
[͵ʌndɚˋlaɪ]... v.... 位於...的下面,置於...之下... 構成...的基礎
[ˋmɪljən]... n.... 百萬,百萬元
[ˋsaɪzmə͵græf]... n.... 地震儀
[ˋsaɪzmɪk]... adj.... 地震的,因地震而引起的
underlie
[͵ʌndɚˋlaɪ]... v.... 位於...的下面,置於...之下... 構成...的基礎
million
[ˋmɪljən]... n.... 百萬,百萬元
53 terms
Calculus 1
Function
Domain
Range
Independent Variable
A rule that assigns to each element in a set A one and only o…
...
...
...
Function
A rule that assigns to each element in a set A one and only o…
Domain
...
10 terms
CALCULUS 1
lim... x→4⁺
lim... x→4⁻
lim... x→4⁻ ... and ... lim... x→4⁺ are not equal
the two sided limit
Values getting closer to 4 ... approaches 4 in a positive direct…
going in the opposite direction... negative direction (3,2,1,0,-…
4 does not exist :(
for a limit to exist, both one sided limits have the same val…
lim... x→4⁺
Values getting closer to 4 ... approaches 4 in a positive direct…
lim... x→4⁻
going in the opposite direction... negative direction (3,2,1,0,-…
34 terms
Calculus 1
Sin(30)
Cos(30)
Tan(30)
Sin(60)
1/2
√3/2
1/√3
√3/2
Sin(30)
1/2
Cos(30)
√3/2
32 terms
Calculus 1
Limits
The Power Rule
Product Rule
Definition of the Derivative
...
...
...
...
Limits
...
The Power Rule
...
21 terms
Calculus 1
slope intercept
m in slope intercept =
b in slope intercept =
point slope form
y=mx+b
slope rise/run
y-intercept
(y-y0)=m(x-x0)
slope intercept
y=mx+b
m in slope intercept =
slope rise/run
32 terms
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…
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
24 terms
Calculus 1 , Chapter 2
Derivitive of y=5x^2 ===
What is derivative of regular number?
Chain rule --- what is (x^2 +3)^6
Derivative product rule
5 times defivitive of x^2
ZERO
2x times 6 (x^2+3)^5
Derivitive of y=5x^2 ===
5 times defivitive of x^2
What is derivative of regular number?
ZERO
14 terms
Trig for Calculus 1
Pythagorean Identity for sin and cos
Pythagorean Identity for tan and sec
Double Angle Identity for sin
Double Angle Identity for cos
sin²θ + cos²θ = 1
tan²θ + 1 = sec²θ
sin(2θ) = 2sinθcosθ
cos(2θ) = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ
Pythagorean Identity for sin and cos
sin²θ + cos²θ = 1
Pythagorean Identity for tan and sec
tan²θ + 1 = sec²θ
6 terms
Calculus - P.1
Testing for x-axis symmetry
Testing for y-axis symmetry
Testing for origin symmetry
Finding y-intercepts
Substitute (x, -y) into the original equation and see if you…
Substitute (-x,y) into the original equation and see if you e…
Substitute (-x, -y) into the original equation and see if you…
Substitute x = 0 into the equation and find y.
Testing for x-axis symmetry
Substitute (x, -y) into the original equation and see if you…
Testing for y-axis symmetry
Substitute (-x,y) into the original equation and see if you e…
9 terms
Calculus 1/21
#1
#2
#3
#4
#1
#2
20 terms
Pre-Calculus Chapter 1
Slope
Point slope form
Slope intercept
General form
m = rise/run = y2 - y1/x2-X1
(y-y1) = m(x-x1)
y = mx + b
0 = Ax + Bx + C
Slope
m = rise/run = y2 - y1/x2-X1
Point slope form
(y-y1) = m(x-x1)
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