MATH31B Midterm 1 Equations

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Calculus - Geometry

user_striner Created by 6 mon ago

Cards in this deck(38)

domain: all real range: all positive

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domain: all positive range: all real

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logbx

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b^x

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(lnb)b^x for b>0

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1/x for x >0

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f'(x)/f(x)

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f(x) grows faster when lim x-->inf f(x)/g(x) = inf or lim x-->inf g(x)/f(x) = 0

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1/sqrt(1-x^2)

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-1/sqrt(1-x^2)

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(-pi/2, pi/2)

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(0, pi)

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[0, pi/2) U (pi/2, pi]

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[-pi/2, 0) U (0, pi/2]

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1 / (1+x^2)

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-1 / (1+x^2)

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1 / |x| sqrt(x^2-1)

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-1 / |x| sqrt(x^2-1)

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

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

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cosh^2x - sinh^2x = 1

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sinh(x)cosh(y) + cosh(x)sinh(y)

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cosh(x)cosh(y)+sinh(x)sinh(y)

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sinh(x)/cosh(x) = (e^x - e^-x)/(e^x + e^-x)

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cosh(x)/sinh(x) = (e^x+e^-x)/(e^x-e^-x)

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1/coshx = 2/(e^x+e^-x)

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1/sinhx = 2/(e^x-e^-x)

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sech^2(x)

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-csch^2(x)

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sech(x)tanh(x)

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-csch(x)coth(x)

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1/sqrt(1+x^2) domain: all real

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1/sqrt(x^2 - 1) domain: x >= 1

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1/1-x^2 domain: |x| < 1

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1/1-x^2 domain: |x| > 1

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-1/x sqrt 1 - x^2 domain: 0 < x <= 1

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-1/|x| sqrt 1 + x^2 domain: x != 0

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integral (x^n)(e^x)dx = x^n(e^x) - n integral x^n-1(e^x)dx

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