Calculus Test 2 Concepts Flashcards

Test Prep

1
Q

lim(as x approaches theta) sin(theta)/theta

A

1

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2
Q

Pythagorean Identity

A

sin^2(theta)+cos^2(theta)=1

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3
Q

Quadratic equations

A

ax^2+bx+c=0

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4
Q

Quadratic Formula

A

(-b+-root(b^2-4ac))/2a

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5
Q

e is the number such that

A

lim (as h approaches 0) (e^n-1)/n=1

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6
Q

d/dx b^x

A

(lnb)b^x

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7
Q

d/dx logbx

A

1/(xlnb), b>0, b!=0, x>0

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8
Q

d/dx lnx

A

1/x

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9
Q

d/dx ln g(x)

A

g’(x)/g(x)

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10
Q

d/dx ln|x|

A

1/x if x!=0

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11
Q

d/dx e^x

A

e^x

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12
Q

d/dx logex

A

1/x

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13
Q

speed is

A

|v|

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14
Q

position is followed by

A

veocity

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15
Q

speed vs velocity

A

velocity has direction

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16
Q

acceleration has a

A

direct correlation of v and a

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17
Q

decceleration has

A

a reverse correlation to v and a

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18
Q

Perimeter

A

add all the sides

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19
Q

Area

A

lw

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20
Q

Area Of A Circle

A

pir^2

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21
Q

Circumference

A

2pir

22
Q

Diameter

A

2r

23
Q

Pythagorean Thm

A

c=root(a^2+b^2); for triable sides

24
Q

Area Of Triangle

A

1/2bh

25
Q

Volume Of Box

A

lwh

26
Q

sinhx

A

(e^x-e^-x)/2

27
Q

coshx

A

(e^x+e^-x)/2

28
Q

tanhx

A

sinhx/coshx

29
Q

cothx

A

coshx/sinhx

30
Q

cothx (variant)

A

1/tanhx

31
Q

sechx

A

1/coshx

32
Q

cschx

A

1/sinhx

33
Q

y=sinhx y-int, domain, type

A

(0,0), R, odd

34
Q

y=coshx y-int, domain, type

A

(0,1), R, even

35
Q

y=tanhx y-int, domain, type

A

(0,0), NA, odd

36
Q

y=sechx y-int, domain, type

A

(0,1), NA, even

37
Q

y=cschx y-int, domain, type

A

y-axis asympt, NA, odd

38
Q

y=cothx y-int, domain, type

A

y-axis asympt, NA, odd

39
Q

sinh(-x)

A

-sinhx

40
Q

cosh(-x)

A

cosh(x)

41
Q

cosh^2x-sinh^2x

A

1

42
Q

1-tanh^2x

A

sech^2x

43
Q

sinh(x+y)

A

sinhxcoshy+coshxsinhy

44
Q

cosh(x+y)

A

coshxcoshy+sinhxsinhy

45
Q

d/dx sinhx

A

coshx

46
Q

d/dx coshx

A

sinhx

47
Q

d/dx tanhx

A

sech^2x

48
Q

d/dx cothx

A

-csch^2x

49
Q

d/dx sechx

A

-secxtanhx

50
Q

d/dx csch

A

-cschxcothx