CALCULUS:GRAPHICAL,NUMERICAL,..-PACKAGE
5th Edition
ISBN: 9780133320381
Author: Finney
Publisher: SAVVAS L
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2. The Riemann sums for a function f on the interval [1, 5]
are given as (2 - u) Ax, where [1, 5] is partitioned
into n subintervals [x-1, X] of width Ax; and u, is some
number in [x,-1, X]. If lim E (2- u) Ax, exists, it
max Ax-0=
equals
(A)
(B) (2- u) Ax
(O(2-rds
(D) 2-ds
Use the definition of area as a Riemann sum (as we did in Section 4.4) to compute
the area between the graph of f(x) = 3x and the x-axis over the interval [2,6]. You may use
the summation formulas (provided elsewhere) to complete this problem. Use right endpoints.
Express the limit lim 2 (c - 4ck) Axk, Wwhere P is a partition of [- 6,8], as a definite integral.
||P|→0k=1
The definite integral is
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- For an element x of an ordered integral domain D, the absolute value | x | is defined by | x |={ xifx0xif0x Prove that | x |=| x | for all xD. Prove that | x |x| x | for all xD. Prove that | xy |=| x || y | for all x,yD. Prove that | x+y || x |+| y | for all x,yD. Prove that | | x || y | || xy | for all x,yD.arrow_forwardProve that every ordered integral domain has characteristic zero.arrow_forwardProve the conjecture made in the previous exercise.arrow_forward
- [Type here] 21. Prove that ifand are integral domains, then the direct sum is not an integral domain. [Type here]arrow_forward= cos t. Let w be a one-form on R. TRUE or FALSE: Consider the function o : [0, 1] –→ [-1, 1] given by ø(t) $* w, [0,7) W = |-1,1] where the intervals [-1, 1] and [0, 7] are understood with the canonical choice of orientation in the direction of increasing real numbers. Select one: O True O Falsearrow_forward
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