# Math Help - Multivariable Calculus Problem

1. ## Multivariable Calculus Problem

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

2. ## Re: Multivariable Calculus Problem

Well for starters, we know the exponential function is always positive.

We know that \displaystyle \begin{align*} -1 \leq \sin{(X)} \leq 1 \end{align*} for all \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 \begin{align*} e^{\sin{(x)}\sin{(y)}} \end{align*} is \displaystyle \begin{align*} \left[ e^{-1} , e^1 \right] \end{align*}.

3. ## Re: 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

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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