What tis the complete domain D and range R of the following multivariable functions: w=2sin xy

Question
Multivariable functions
asked 2021-01-31
What tis the complete domain D and range R of the following multivariable functions:
\(\displaystyle{w}={2}{\sin{{x}}}{y}\)

Answers (1)

2021-02-01
\(\displaystyle{w}={2}{\sin{{x}}}{y}\)
Domain for sine function is real numbers.
Thus, \(\displaystyle{D}=\mathbb{R}{2}\)
Now,\(\displaystyle−{1}\le{\sin{\theta}}\le{1}\)
\(\displaystyle−{1}\le{\sin{{x}}}{y}\le{1}\)
\(\displaystyle−{1}\times{2}\le{2}{\sin{{x}}}{y}\le{1}\times{2}\)
\(\displaystyle−{2}\le{\sin{{x}}}{y}\le{2}\)
So, \(\displaystyle{R}={\left[−{2},{2}\right]}\)
0

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