# Multivariable Calculus Problem

• Feb 25th 2013, 06:45 PM
clintonh0610
Multivariable Calculus Problem
What is the range of e(sinx)(siny) and how do you figure it out? Thanks!
• Feb 25th 2013, 07:37 PM
Prove It
Re: 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 PM
fashionsport
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

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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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