Math problem

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Anonymous

Math problem 2016-02-04 23:40:30 Post No. 49750

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Math problem 2016-02-04 23:40:30 Post No. 49750

[Report] Image search: [iqdb] [SauceNao] [Google]

Hey guises?

Wanna do some math?

Got some basic Calculus question for you.=^)

Try them if you got them skillz

Protip: Hospital rule.

GLHF =^)

>>

first Lim is Pi btw

>>

Every day this site is becoming more cancerous

>>

2)

cos(sqrt(x))^(3/x)

= exp((3/x)*ln(cos(sqrt(x))))

= exp((3/x)*ln(1-x/2 + o(x)))

= exp((3/x)*(-x/2)+o(x))

lim (x ->0) = exp(-3/2)

>>

>>49750

In the third one, replace tan x with its Taylor polynomial approximation: tan x = x + x^3 / 3 + ..., so tan x / x = 1 + x^2 / 3 + ..., and replacing 1/x^2 with n, you get (1 + (1/3) * (1/n))^n, the limit of which is e^(1/3)

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