The Leaning Tower of Suurhusen is a medieval steeple in Suurhasen, Germany. The tower leans at an angle of 5.1939 ° from the vertical. (In comparison, the Leaning Tower of Pisa leans at an angle of 3.97 ° .) The angle of elevation to the top of the tower is 44.2 ° when measured 100 ft from the base of the tower. Find the distance h from the base of the tower to the top of the tower. Round to the nearest tenth of a foot.
The Leaning Tower of Suurhusen is a medieval steeple in Suurhasen, Germany. The tower leans at an angle of 5.1939 ° from the vertical. (In comparison, the Leaning Tower of Pisa leans at an angle of 3.97 ° .) The angle of elevation to the top of the tower is 44.2 ° when measured 100 ft from the base of the tower. Find the distance h from the base of the tower to the top of the tower. Round to the nearest tenth of a foot.
The Leaning Tower of Suurhusen is a medieval steeple in Suurhasen, Germany. The tower leans at an angle of
5.1939
°
from the vertical. (In comparison, the Leaning Tower of Pisa leans at an angle of
3.97
°
.) The angle of elevation to the top of the tower is
44.2
°
when measured
100
ft
from the base of the tower. Find the distance
h
from the base of the tower to the top of the tower. Round 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).
Elementary Statistics: Picturing the World (7th Edition)
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