Chapter 12: Q 6. (page 930)

If $g : R^{3} \to R$ is continuous at the point $(a, b, c) a n d C$ is a curve in $R^{3}$ containing the point $(a, b, c)$ ,what can we say about $\lim_{\underset{C}{(x, y, z) \to (a, b, c)}} g (x, y, z) ?$

Short Answer

Expert verified

The limit evaluates the output value to which the function approaches as input approaches the given point.

Step by step solution

Given Information

The given limits are $\lim_{\underset{C}{(x, y, z) \to (a, b, c)}} g (x, y, z)$ , where C is a curve in containing the point $(a, b, c)$

Conclusion from these limits.

The output that the function tends to approach as the input approaches the point is determined by evaluating the function's limit at a point. The path of approach is irrelevant for determining the limit unless it passes via the input location. As a result, regardless of the approach path, the limiting value will remain constant. The function may or may not travel through the point as well. It's conceivable that the function is now uncertain. As the input approaches the designated point, the limit evaluates the output value to which the function approaches.

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If $g : R^{3} \to R$ is continuous at the point $(a, b, c) a n d C$ is a curve in $R^{3}$ containing the point $(a, b, c)$ ,what can we say about $\lim_{\underset{C}{(x, y, z) \to (a, b, c)}} g (x, y, z) ?$

Short Answer

Step by step solution

Given Information

Conclusion from these limits.

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If g:R3→Ris continuous at the point (a,b,c)andCis a curve in R3containing the point (a,b,c),what can we say about lim(x,y,z)→(a,b,c)Cg(x,y,z)?

Short Answer

Step by step solution

Given Information

Conclusion from these limits.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

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Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

If $g : R^{3} \to R$ is continuous at the point $(a, b, c) a n d C$ is a curve in $R^{3}$ containing the point $(a, b, c)$ ,what can we say about $\lim_{\underset{C}{(x, y, z) \to (a, b, c)}} g (x, y, z) ?$