Let a be a nonzero constant. Prove that if lim x→0 f(x) = L then lim x→0 f(ax) = L.. b. Show by means of an example that a must be nonzero
Limits
Let a be a nonzero constant. Prove that if lim x→0
f(x) = L then lim x→0
f(ax) = L..
b. Show by means of an example that a must be nonzero
Chapter 2
4. An astronaut standing on the moon throws a rock into the air. The height of the rock is
s = −(27/10) t^2 + 27t + 6
where s is measured in feet and t is measured in seconds.
a. Find expressions for velocity and acceleration of the rock.
b. Find the time when the rock is at its highest point. What is the height of the rock at this time?
c. Find the total time that the rock spend on the air.
Chain Rule
a. Show that the derivative of an odd function is even. That is, if f(-x) = -f(x), then f(−x) =-f′(x).
b. Show that the derivative of an even function is odd. That is, if f(-x) = f(x), then f(−x) =-f′(x).
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