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What is the instantaneous velocity at t=2 seconds? Calculate this by finding the limit as

h→0 of the average velocity 3h−6.

A.lim h→0 (3h−6)
B. lim h→0 3h−6/h
​C. lim h→2 (3h−6)
D. lim h→2 3h−6/h


1 Answer

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Final answer:

The instantaneous velocity at t = 2 seconds is calculated by evaluating the limit as h approaches 2 of the expression 3h - 6/h. When this limit is determined, the result is 3 m/s, representing the instantaneous velocity at that moment.

Step-by-step explanation:

The question asks for the instantaneous velocity at a specific point in time, which is a concept from calculus. To find the instantaneous velocity at t = 2 seconds, we need to determine the derivative of the position function at that time. However, the expression provided, 3h −6, appears to represent a change in position over a small interval of time described by h. The correct approach to finding the instantaneous velocity involves taking the limit of the average velocity as h approaches zero, which means we should evaluate the option D: lim h →2 3h−6/h. Upon calculation, we find:

lim h →2 (3h−6)/h = lim h →2 3−6/h

As h approaches zero, the term −6/h becomes undefined; however, since it is not dependent on h, it has no effect on the limit of the function as h approaches zero. Therefore, the limit simplifies to the coefficient of h, which is 3. Thus, the instantaneous velocity at t = 2 seconds is 3 m/s.

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