What is the range of e^{(sinx)(siny)}and how do you figure it out? Thanks!

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- Feb 25th 2013, 06:45 PMclintonh0610Multivariable Calculus Problem
What is the range of e

^{(sinx)(siny)}and how do you figure it out? Thanks! - Feb 25th 2013, 07:37 PMProve ItRe: Multivariable Calculus Problem
Well for starters, we know the exponential function is always positive.

We know that $\displaystyle \displaystyle \begin{align*} -1 \leq \sin{(X)} \leq 1 \end{align*}$ for all $\displaystyle \displaystyle \begin{align*} X \end{align*}$, so that means the product of two sine functions is also going to be bounded between these two values.

Therefore the range of $\displaystyle \displaystyle \begin{align*} e^{\sin{(x)}\sin{(y)}} \end{align*}$ is $\displaystyle \displaystyle \begin{align*} \left[ e^{-1} , e^1 \right] \end{align*}$. - Feb 25th 2013, 10:23 PMfashionsportRe: Multivariable Calculus Problem
Thanks so much! That's exactly what I was looking for

Btw do you mind clarifying your first sentence? As in, why should you write just (-∞, 0)∪(0, 9) and not x∈(-∞, 0)∪(0, 9)? Thanks again

!!!

EDIT: Or I guess what I mean is, how do you define your variable with interval notation? It seems no one ever says "x" anywhere when they say their answer in interval notatio

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Thanks so much! That's exactly what I was looking for

Btw do you mind clarifying your first sentence? As in, why should you write just (-∞, 0)∪(0, 9) and not x∈(-∞, 0)∪(0, 9)? Thanks again

!!!

EDIT: Or I guess what I mean is, how do you define your variable with interval notation? It seems no one ever says "x" anywhere when they say their answer in interval notatio

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