Calculus I

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Exam review

Problem 15

R=8

V(t) = pi(R²)

V(t) = pi*8^2h = pi*64h

V^’(t) = 64pi*h^’(t) = 2/64pi = 1/32 pi m/min

Does anyone have trouble with this problem?

Welcome calculus students. Calculus is the study of change, in particular how the values of a function change as the input variable(s) change(s). In calculus I, the focus is on studying the rate of change, namely how fast the values are changing. This speed corresponds to the slope of the tangent line to the curve. A physical example is the study of how a particle moves in a straight line and its velocity, which is the speed of the particle together with the direction.

The graph plotted for the website is a taking some of these ideas to 3 dimensions. In particular, you are being shown a series of tangent planes (planes which touch a surface locally in one point). Such as series could be part of a numeric (approximate) solution to a particle moving across a surface subject to a force field.