Indeterminate and none-indeterminate forms + Other stuff I kept forgetting

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When do you apply L’Hopital?

Get a hint
Hint

For indeterminate forms

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0-

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Hint

not indeterminate

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52 Terms

1
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When do you apply L’Hopital?

For indeterminate forms

2
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0-

not indeterminate

3
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∞+∞

not indeterminate

4
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0×1

not indeterminate

5
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∞^∞

not indeterminate

6
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∞/∞

indeterminate

7
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0/0

indeterminate

8
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∞^0

indeterminate

9
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1^

indeterminate

10
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0*

indeterminate

11
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0^0

indeterminate

12
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0/

not indeterminate

13
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∞+∞

not indeterminate

14
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∞-∞

indeterminate

15
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1*

not indeterminate

16
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How do you find the inflection points?

f”(x)=0

17
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f(x) is continuous on the closed interval [a,b] then…

it’s differentiable on (a,b) and integrable on [a,b]

18
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Cube

Volume: s³ Surface Area: 6s²

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Rectangle Prism + Rectangle

Volume: LWH Surface Area: 2LH+2LW+2WH

A: LW Perimeter: 2(L+W)

20
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Cone

Volume: 1/3π r²h

Surface Area: πr(r+√h²+r²)

21
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Triangular Prism

Volume: BH Surface Area: 2HB+B²

22
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Triangle

Area: ½BH

23
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Cylinder

Volume: πr²h Surface Area: 2πrH+2πr²

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Sphere

Volume: 4/3 πr³
Surface Area: 4πr³

25
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f’(x)=cosx

-sinx

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f’(x)=sinx

cosx

27
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f’(x)=tanx

sec²x

28
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f’(x)=cot

-csc²x

29
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f’(x)=secx

secxtanx

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f’(x)=cscx

-cscxcotx

31
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d/dx(arcsinx)

1/√(1-x²)

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d/dx(arccosx)

-1/√1-x²

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d/dx(arctanx)

1/(1+x²)

34
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d/dx(arccotx)

-1/(1+x²)

35
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d/dx(arcsecx)

1/(|x|√x²-1)

36
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d/dx(arccscx)

-1/(|x|√1-x²)

37
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turn tan(x) into

sin(x)/cos(x)

38
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f(x)=x³ (-inf,inf)

no abs. max/min

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f(x)=1/x²+1 (-inf,inf)

abs max no abs mini

40
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f(x)=tan(x) (-pi/2,pi/2)

no abs max/min

41
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Extreme Value Theorem

f is continous [a,b], there is a point within it that has an abs max and abs min

42
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Fermat’s Theorem

If f has a local extremum at c and f differentiable at c means f’©=0 or f’©=Undef

43
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Local extrema at f’©=Undef

-abs value x

-cusp

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semi circle

Area: πr2/2

Perimeter: πr+2r

45
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No local extrema at f’©=0

x³ with f’©=0 being horizontal

46
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No local extrema at f’©=Undefined

∛x f’©=Undef horizontal

47
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<p>What’s this</p>

What’s this

ln(x) and e^x function graph

48
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<p>What’s this</p>

What’s this

f(x)=√x sq root function graph

49
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<p>What’s this </p>

What’s this

f(x)=∛x cube root function graph

50
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<p>What’s this</p>

What’s this

f(x)=1/x reciprocal function graph

51
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<p>What’s this </p>

What’s this

f(x)=1/x² rational function graph

52
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<p>Graph equation for a circle</p>

Graph equation for a circle

x²+y²=r²