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6.1 ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY

1. The function f(x) = 2x has only one antiderivative.
2. Using a graph of f' (the derivative of a function, f) is is possible to sketch an approximate graph of f.
3. In Example 2, the antiderivative, F(x), is always increasing.
4. Where f' (the derivative) has a maximum, f (the function) has a critical point.
5. The Fundamental Theorem of Calculus can be used to express values of f(x) in terms of definite integrals.

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6.2 CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY

1. The antiderivative of a sum is the sum of the antiderivatives of the summands.
2. The antiderivative of a power of x is always a power of x.
3. According to the book, the antiderivatives of the sine and cosine are easy to guess.
4. Antiderivatives can be checked by evaluation.
5. An antiderivative of sin x + 3 cos x is cos x - 3 sin x + 7.
6. Antiderivatives can always be used to compute definite integrals.

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6.3 DIFFERENTIAL EQUATIONS

1. The equation of motion s = 50t is the only solution to the differential equation ds/dt=50.
2. An object thrown vertically upward moves with uniformly accelerated motion.
3. The object in Example 2 reaches its highest point when t = 9.8/10 = .98 sec.
4. An initial-value problem always has a unique solution.
5. The solution to a differential equation is actually a family of functions.

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6.4 SECOND FUNDAMENTAL THEOREM OF CALCULUS

1. The definite integral can be used to construct antiderivatives.
2. The limits in a definite integral must be constants.
3. The dark region in Figure 6.18 represents f(x+h) - f(x).
4. The height of the dark region in Figure 6.19 is approximately f(x)
5. For all numbers x except 0 Si(x) = sin(x)/x