FundamentalTheorem of Calculus

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December 9, 2022

FundamentalTheorem of Calculus

Description

1. (5 pts) Letp >0.Find the limit by applying the FundamentalTheorem of Calculus to an appropriate integral.limn→∞1p+ 2p+…+npnp+1.2. (5 pts) Suppose thatfis a continuous 1-1 function on [0,1],and∫10f(x)dx= 3.Which of the following are possible?(A)f(0) = 0, f(1) = 2;(B)f(0) = 6, f(1) = 4;(C)f(0) = 2, f(1) = 9;(D)f(0) = 3, f(1) =−3.3. (5 pts) Compute the limit:limx→0+∫sinx0√tanx dx∫tanx0√sinx dx