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By the MVT, we know that there is at least one c sin b − sin a sin such that = cos c. We know cos c ≤ 1 for all c. Therefore, − a. − sin a ≤ 1, − a. sin a − sin b ≤ 1, and sin a − sin b ≤ a − b . a − b. Create your own worksheets like this one with Infinite Calculus.
For each problem, find the average value of the function over the given interval. Then, find the values of c that satisfy the Mean Value Theorem for Integrals.
Introduction to Differential Equations. Separable Equations. Exponential Growth and Decay. Free Calculus worksheets created with Infinite Calculus. Printable in convenient PDF format.
Mean Value Theorem, Rolle's Theorem. For each problem, determine if the Mean Value Theorem can be applied. If it can, find all values of c that satisfy the theorem. If it cannot, explain why not. -x2 + 1. 1) y = ; [1, 6] 3x. x2. 3) y = ; [-6, -3] 4x + 8. 2.
For each problem, find the average value of the function over the given interval. Then, find the values of c that satisfy the Mean Value Theorem for Integrals.
Test and Worksheet Generator for Calculus. Infinite Calculus covers all of the fundamentals of Calculus: limits, continuity, differentiation, and integration as well as applications such as related rates and finding volume using the cylindrical shell method.
MVTI; Average Value of a Function. For each problem, find the values of c that satisfy the Mean Value Theorem for Integrals. 1) f (x) = 2x2 - 4x - 4; [0, 3] For each problem, find the average value of the function over the given interval. 2) f (x) = -x2 + 2x + 1; [1, 4]
