When you answer can you please show how you got it? Thank you 1. Write the Inver

Question

When you answer can you please show how you got it? Thank you
1. Write the Inverse function of y=e^x
2. Solve the following for theta: 2sin^2(theta) = 1 on the interval [0,2(pi)] 3. Evaluate ln(1) without a calculator I took a quiz in Calculus with these and various other questions on it and I have the chance to retake it for no penalty (the whole class pretty much failed) 2. Solve the following for theta: 2sin^2(theta) = 1 on the interval [0,2(pi)] 3. Evaluate ln(1) without a calculator I took a quiz in Calculus with these and various other questions on it and I have the chance to retake it for no penalty (the whole class pretty much failed)

Explanation / Answer

inverse function ... swap x an y - solve for y y = e^x x = e^y ( take ln of both sides) ln|x|=y ( but e^y > 0 thus x >0 ) ln(x) =y y = ln(x) 2[sin(x)]^2=1 (divide by 2)(x easier than theta so I sub) [sin(x)]^2=(1/2) (root bot sides) sin(x) = root(1/2) (use inverse sine) x = arcsine[root(1/2)]=pi/4 but arcsine function only defined on [-pi/2,pi/2] adding pi ... 3pi/4 is also a solution let y = ln(1) (use base e on both sides) e^y = 1 ( a^0=1) y=ln(1)=0

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