Ex 2.1, 1 Find principal value of sin1 (1/2) Chapter 2


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Limit of (1+1/x)^x as x approaches ∞

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Ex 2.1, 1 Find principal value of sin1 (1/2) Chapter 2

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Understanding the Limit as x Approaches Infinity Outlier

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Algebra Simplify (x-i) (x+i) (x − i) (x + i) ( x - i) ( x + i) Expand (x−i)(x+i) ( x - i) ( x + i) using the FOIL Method. Tap for more steps. x⋅x+xi− ix−ii x ⋅ x + x i - i x - i i Simplify terms. Tap for more steps. x2 + 1 x 2 + 1


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Say we want to find a value for x which makes this equal to i, so want cos(x) = 0 and sin(x) = 1. x = pi/2 is a value which satisfies this. So e^(i*pi/2) = i. So now that we have this seemingly more complicated way of writing i, we can substitute it for the base of our exponent and raise it to the power of i. So we get (e^(i*pi/2))^i.


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