Explanation Given information: 3 ≤ f ( x ) ≤ 4 and 0 ≤ x ≤ 5 Explanation: By applying integration on 3 ≤ f ( x ) ≤ 4 from x = 0 to x = 5 ⇒ ∫ 0 5 3 ≤ ∫ 0 5 f ( x ) ≤ ∫ 0 5 4 ⇒ 3 x | 0 5 ≤ ∫ 0 5 f ( x )

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Chapter 6, Problem 65RE

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Whether the statement is true or false, “If 3 ≤ f(x) ≤4 where 0≤ x ≤5 then 3 ≤ 15∫05f(x) ≤4”.

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Chapter 6, Problem 64RE

Chapter 6, Problem 66RE

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(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro

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CALCULUS+ITS APPL.,BRIEF-MYLAB MATH

Ch. 6.1 - Determine the following: a. t7/2dt b....Ch. 6.1 - Find a function f(t) that satisfies f(t)=3t+5 and...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Determine the following: 4x3dx Ch. 6.1 - Determine the following: 13xdx

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Whether the statement is true or false, “If 3 ≤ f ( x ) ≤ 4 where 0 ≤ x ≤ 5 then 3 ≤ 1 5 ∫ 0 5 f ( x ) ≤ 4 ”.

Solution Summary: The author analyzes whether the statement is true or false by applying integration on 3le.

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Whether the statement is true or false, “If 3 ≤ f(x) ≤4 where 0≤ x ≤5 then 3 ≤ 15∫05f(x) ≤4”.

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Chapter 6 Solutions