Approximation (a) Find lim x → 0 1 − cos x x 2 . (b) Use your answer to part (a) to device the approximation cos x ≈ 1 − 1 2 x 2 for x near 0. (c) Use your answer to part (b) to approximate cos(0.1). (d) Use a calculator to approximate cos(0.1) to four decimal places. Compare the result with part (c).
Approximation (a) Find lim x → 0 1 − cos x x 2 . (b) Use your answer to part (a) to device the approximation cos x ≈ 1 − 1 2 x 2 for x near 0. (c) Use your answer to part (b) to approximate cos(0.1). (d) Use a calculator to approximate cos(0.1) to four decimal places. Compare the result with part (c).
Solution Summary: The author explains the value of the limit undersetxto 0mathrmlim
As a wave passes by an offshore piling, the height of the water is modeled by the function
3 cos (+)
20
where h(t) is the height in feet above mean sea level at time t seconds.
h(t) = 3 cos
trough
crest
(a) Find the period of the wave.
s
(b) Find the wave height, that is, the vertical distance between the trough and the crest of the wave.
ft
The height above the ground of a rider on a Ferris wheel can be modelled by the sinusoidal function
h=4sin(3.44t+0.58)+13
where hℎ is the height of the rider above the ground, in metres, and t is the time, in minutes, after the ride starts
Based on the sinusoidal function, the maximum height of the rider above the ground, to the nearest meter, is
An alternating current is described by the function
i(t) = – 13 sin(450t + 40°) milliamperes,
where t is the time measured in seconds.
Paying close attention to the units and rounding to the nearest hundredth, determine
each of the following values.
(a) Maximum current in milliamperes:
(b) Period in milliseconds:
(c) Phase shift in milliseconds
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.