Explanation Given information: Given indefinite integral is ∫ ( x 3 + 5 x 2 + 6 ) d x . Calculation: The integral of a function of the form x n is given by ∫ x n d x = x n + 1 n + 1 + C where n â‰ -1 The function can be written as: ∫ ( x 3 + 5 x 2 + 6 ) d x = ∫ x 3 d x + ∫ 4 x 2 d x + ∫ 6 d x ∫ ( x 3 + 5 x 2 + 6 ) d x = ∫ x 3 d x + 4 ∫ x 2 d x + 6 ∫ x 0 d x Using the above rule, ∫

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Author: DA

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Chapter 6.2, Problem 67P

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To find the indefinite integral of the given function.

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Chapter 6.2, Problem 66P

Chapter 6.2, Problem 68P

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3. True False. If false create functions that prove it is false. Note: f(x) = g(x). a) If_lim ƒ(x) = ∞ and_lim g(x) = ∞,then_lim [ƒ(x) − g(x)] = 0 x→ 0+ x→0+ x→0+ b) If h(x) and g(x) are continuous at x = c, and if h(c) > 0 and g(c) = 0, then h(x) lim. will = x→c g(x) c) If lim f(x) = 0 and lim g(x) = 0 then lim f(x) does not exist. x-a x-a x→a g(x)

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15. a) Consider f(x) = x-1 3x+2 and use the difference quotient to determine the simplified expression in terms of x, for the slope of any tangent to y = f(x). Also, determine the slope at x = 2. 15 b) Determine the equation of the tangent to f(x) at x = 2. Final answer in Standard Form Ax + By + C = 0, A ≥ 0, with no fractions or decimals.

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To find the indefinite integral of the given function.

Solution Summary: The author explains how to determine the indefinite integral of a function of the form x n.

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Chapter 6 Solutions