calc final things to know

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Last updated 9:32 PM on 4/30/26
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20 Terms

1
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1/(1-x)

R=1

<p>R=1</p>
2
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e^x

R= infinity

<p>R= infinity</p>
3
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ln(1+x)

R =1

<p>R =1</p>
4
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(1+x)^k

R=1

<p>R=1</p>
5
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sin(x)

R = infinity

<p>R = infinity</p>
6
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cos(x)

R = infinity

<p>R = infinity</p>
7
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arctan(x)

R =1

<p>R =1</p>
8
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sin²x

((1-cos(2x))/2

9
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cos²x

((1+cos(2x))/2

10
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<p>if </p>

if

x=a*sin(theta)

11
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<p>if</p>

if

x= a*tan(theta)

12
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<p>if</p>

if

x = a*sec(theta)

13
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arclength of f(x)

integral of sqrt(1+f’(x)²)

14
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arclength of polar curve

integral of sqrt(r²+r’²)

15
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arclength of parametric curve

integral of sqrt(x’²+y’²)

16
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area of polar curve

1/2*integral of (r²)

17
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area of parametric curve

integral of (y(t)*x’(t))

18
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real root

c1*e^r1*x+ c2*e^r2*x

19
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repeated roots

c1e^rx+ c2xe^rx

20
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imaginary root

e^ax(c1cos(bx)+c2sin(bx))