Free-Falling Object In Exercises 103 and 104, use the position function s ( t ) = − 4.9 t 2 + 200 , which gives the height (in meters) of an object that has fallen for t seconds from a height of 200 meters. The velocity at time t = a seconds is given by lim t → a s ( a ) − s ( t ) a − t At what velocity will the object impact the ground?
Free-Falling Object In Exercises 103 and 104, use the position function s ( t ) = − 4.9 t 2 + 200 , which gives the height (in meters) of an object that has fallen for t seconds from a height of 200 meters. The velocity at time t = a seconds is given by lim t → a s ( a ) − s ( t ) a − t At what velocity will the object impact the ground?
Solution Summary: The author calculates the velocity of a can of paint when it touches the ground.
Free-Falling Object In Exercises 103 and 104, use the position function
s
(
t
)
=
−
4.9
t
2
+
200
, which gives the height (in meters) of an object that has fallen for t seconds from a height of 200 meters. The velocity at time
t
=
a
seconds is given by
lim
t
→
a
s
(
a
)
−
s
(
t
)
a
−
t
At what velocity will the object impact the ground?
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Does the series converge or diverge
Chapter 1 Solutions
Calculus Of A Single Variable With Calcchat And Calcview, 11e
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