How long will it take until our measurements of the coffee’s temperature are indistinguishable from room temperature?

Background: When a function f(t) represents some real-world quantity, its limit as 𝑡→∞t→∞ represents the “long-term” behavior. Often, this kind of limit can be evaluated through algebraic methods. However, in more difficult cases, limits can be evaluated in terms of their individual parts by applying limit laws . As we now know, limits involving infinity […]

Explain what you are doing and why you are doing it. For example, if have to use reduction then explain WHAT is being reduced. For example, what is a standard integral? And most of all WHEN and HOW do we simplify in these questions?

Explain what you are doing and why you are doing it. For example, if  have to use reduction then  explain WHAT is being reduced. For example, what is a standard integral? And most of all WHEN and HOW do we simplify in these questions? The questions are in the Word document called “calc homework”. It […]

Review problem. Find and classify the critical points of f(x, y) = 10x + x2y − xy −6y.

Each problem is worth 3 points. Be sure to follow the guidelines. 1. Find a parameterization of the part of the plane plane 2x + 3y + z = 6 that lies in the first octant. 2. The equation x2 A + y2 B + z2 C = 1 defines a shape called an ellipsoid. […]

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