A 40 -ft boom on a crane is attached to the crane platform at point D . A cable is attached to the end of the boom at point B and to a 12 -ft A-frame at point A anchored by the counter weight. If ∠ B D A is 85.2 ° , find the length of the cable to the nearest tenth of a foot.
A 40 -ft boom on a crane is attached to the crane platform at point D . A cable is attached to the end of the boom at point B and to a 12 -ft A-frame at point A anchored by the counter weight. If ∠ B D A is 85.2 ° , find the length of the cable to the nearest tenth of a foot.
Solution Summary: The author calculates the length of the cable attached to a 12ft frame, with the angle between the frame and the boom being 85.2°.
A
40
-ft
boom on a crane is attached to the crane platform at point
D
. A cable is attached to the end of the boom at point
B
and to a
12
-ft
A-frame at point
A
anchored by the counter weight. If
∠
B
D
A
is
85.2
°
, find the length of the cable to the nearest tenth of a foot.
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).
University Calculus: Early Transcendentals (4th Edition)
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