----- (1 pt) Given the function f(x) = 1/x^1/2 (in blue), consider the functions
ID: 2838295 • Letter: #
Question
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(1 pt) Given the function f(x) = 1/x^1/2 (in blue), consider the functions g(in green) arid h (in red) graphed below which are continuous on (0, infinity ). Assuming the graphs continues in the same way as x goes to infinity, answer the following questions. 1. Does the improper integral int 1 to infinity f( x) dx converge, diverge, or not sufficient information? 2. Does the improper integral int 1 to infinity g (x) dx converge, diverge, or not sufficient information? 3. Does the improper integral int 1 to infinity h (x) dx converge, diverge, or not sufficient information? (1 pt) Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as inf. If it diverges to negative infinity, state your answer as -inf. If it diverges without being infinity or negative infinity, state your answer as div. (1 pt) A hawk flying at 15m/s at an altitude of 172 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation until it hits the ground, where y is its height above the ground and x is the horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground. Answer:Explanation / Answer
1. f(x) diverges.
2. Because f(x) diverges, a function with a larger slope will also diverge; thus, g(x) also diverges.
3. There is not enough information to say whether h(x) will converge or diverge.
4. The integral diverges to infinity.
5. The prey will hit the ground when altitude (y) is equal to zero; thus,
0 = 172 - (x^2)/45
(x^2)/45 = 172
x^2 = 7740, x = 88 m
Thus, the prey travels a distance of 88 meters.
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