Question: User: Question 5
Use the formula A = πr² for the area of the circle to find:
a) The average rate of which the area of a circle changes with r as the radius increases from r = 2
to r = 4.
b) The instantaneous rate at which the area of a circle changes with r when r = 4.
Question 6
Use the definition of the derivative to find f'(x) and then find the tangent line to the graph of
y = f(x) at x = a.
a) f(x) = 2x²; a = 1.
b) f(x) = √(x + 1); a = 8.
graph/math position_hint: top-left — text block with Question 5 and formula A = πr²; center-left — parts a) and b) asking average and instantaneous rate of change for a circle area with r increasing from 2 to 4 and at r = 4; bottom-left — Question 6 with derivative definition, tangent line to y = f(x) at x = a, and examples f(x)=2x² at a=1 and f(x)=√(x+1) at a=8.
Question 5 Use the formula A = πr² for the area of the circle to find: a) The average rate of which
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