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7) Continuous means the limit must be the same at every point from both directions. In these cases you just need to pick k such that the two piecewise parts are equal at the points where the two parts meet (so x = 3, x = 4 for the two problems).
8) V = (4/3)pi R^3
dV/dt = 4 pi R^2 dR/dt (by chain rule)
dV/dt = 100 ft^3 / min
A) let R = 5, solve for dR/dt
B) SA = 4 pi R^2
dSA/dt = 8 pi R * dR/dt
Plug in, solve for dSA/dt.
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