- #1

toforfiltum

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## Homework Statement

Function is ##lim_{(x,y,z) \rightarrow (0,\sqrt\pi,1)} \ e^{xz} \cos y^2 - x##

## Homework Equations

## The Attempt at a Solution

As ##x \rightarrow 0## along ##y= \sqrt \pi, z=1##, ##f(x,y,z)= -1##

As ##y \rightarrow 0## along ##x=0, z=1##, ##f(x,y,z) = -1##

As ##z \rightarrow 1## along ##x=0, y= \sqrt \pi##, ##f(x,y,z) = -1##

From what I have done, the limit looks like it is -1. I'm wondering if there are any other functions I could use to show that it is true. Or this is not needed at all, because of the argument that the function is continuous at the point ##(0,\sqrt \pi, 1)##? If so, the above steps are not needed at all, right?

Thanks.

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