Question
b) If
is continuous at the origin.
Answer :
Word Count : 286
To check if the given function \[ f(x,y) = \begin{cases} x \sin\left(\frac{1}{y}\right) + y \sin\left(\frac{1}{x}\right), & \text{if } xy \neq 0 \\ 0, & \text{if } xy = 0 \end{cases} \] is continuous at the origin \((0,0)\), we need to check if: \[ \lim\limits_{(x,y) \to (0,0)} f(x,y) = f(0,0) = 0. \] ### Step 1: Evaluate along _______ ___ ________ _________ ___.
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To check if the given function \[ f(x,y) = \begin{cases} x \sin\left(\frac{1}{y}\right) + y \sin\left(\frac{1}{x}\right), & \text{if } xy \neq 0 \\ 0, & \text{if } xy = 0 \end{cases} \] is continuous at the origin \((0,0)\), we need to check if: \[ \lim\limits_{(x,y) \to (0,0)} f(x,y) = f(0,0) = 0. \] ### Step 1: Evaluate along _______ ___ ________ _________ ___.
_____ ________ __________ _______ __________ ______.
_____ ________ ___ _____ ___ __________ ____ _____ _______.
_________ ___ __________ ___ ______ ____ ______.
____ ____ _____ _______ ________ ____ _____ ___ ______ ________.
___ ________ ________ ____ ________ _____ __________ _________ __________ _________ _______.
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Related Questions
State whether the following statements are true or false. Justify your answer.
a) is in
form.
e) The function is locally invertible at
e) The function is integrable on ]2,1[ × ]3,1
c) Find fog and gof, if they exist, for the functions
c) Prove that
b) is a homogeneous function of degree
d) The function
is locally invertible at
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