Questions from General Calculus


Q: Refer to Fig. 5 and evaluate 0∫3 f (

Refer to Fig. 5 and evaluate 0∫3 f (x)dx. Figure 5:

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Q: Refer to Fig. 6 and evaluate -1∫1 f

Refer to Fig. 6 and evaluate -1∫1 f (t)dt. Figure 6:

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Q: Refer to Fig. 7 and evaluate -1∫2 f

Refer to Fig. 7 and evaluate -1∫2 f (t)dt. Figure 7:

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Q: A rock is dropped from the top of a 400-foot

A rock is dropped from the top of a 400-foot cliff. Its velocity at time t seconds is υ(t) = -32t feet per second. Find the displacement of the rock during the time interval 2 ≤ t ≤ 4.

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Q: The velocity at time t seconds of a ball thrown up into

The velocity at time t seconds of a ball thrown up into the air is υ(t) = -32t + 75 feet per second. (a) Find the displacement of the ball during the time interval 0 ≤ t ≤ 3. (b) Given that the initia...

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Q: The velocity at time t seconds of a ball thrown up into

The velocity at time t seconds of a ball thrown up into the air is υ(t) = -32t + 75 feet per second. (a) Compute the displacement of the ball during the time interval 1 ≤ t ≤ 3. (b) Is the position of...

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Q: The velocity of a skydiver at time t seconds is υ(

The velocity of a skydiver at time t seconds is υ(t) = 45 - 45e-0.2t meters per second. Find the distance traveled by the skydiver the first 9 seconds.  

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Q: Let f (x, y) = x2 - 3xy -

Let f (x, y) = x2 - 3xy - y2. Compute f (5, 0), f (5,-2), and f (a, b).

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Q: Let f (x, y) = 10x2/5y3/

Let f (x, y) = 10x2/5y3/5. Show that f (3a, 3b) = 3f (a, b).

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Q: Find all points (x, y) where f (x

Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f (x, y) at each of these points. If the...

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