Presentation on Weierstrass M-Test
... Any sequence that satisfies the Cauchy Criterion is known as a Cauchy sequence. The above theorem also shows that every convergent sequence is Cauchy, and every Cauchy sequence is convergent. COROLLARY 1: If is a Cauchy sequence that converges to Z, and N is chosen such that every such that , then f ...
... Any sequence that satisfies the Cauchy Criterion is known as a Cauchy sequence. The above theorem also shows that every convergent sequence is Cauchy, and every Cauchy sequence is convergent. COROLLARY 1: If is a Cauchy sequence that converges to Z, and N is chosen such that every such that , then f ...
![MAT 16A Homework 12 Section 3.2 [1] Given function f(x) =](http://s1.studyres.com/store/data/006685359_1-9a5c1caa3b9f699c577b4c37de25b65e-300x300.png)
MAT 16A Homework 12 Section 3.2 [1] Given function f(x) =
... Sign of f (x) f (−2) = 4 > 0 f 2 = −3 < 0 f (2) = 34 > 0 Conclusion Increasing Decreasing Increasing By first derivative test, x = −1 is a relative maxima, and x = 1 is a relative minima. Remark: The function f (x) = x + x1 is undefined at x = 0. So more precisely, we should not consider the interva ...
... Sign of f (x) f (−2) = 4 > 0 f 2 = −3 < 0 f (2) = 34 > 0 Conclusion Increasing Decreasing Increasing By first derivative test, x = −1 is a relative maxima, and x = 1 is a relative minima. Remark: The function f (x) = x + x1 is undefined at x = 0. So more precisely, we should not consider the interva ...
Practice with Proofs
... according to whether x ≤ 1 or x > 1. A lot of the time you can take y = x. 2. The problem is asking you to prove that ∃x∀y : y 2 ≥ x. What number is less than or equal to all squares? 3. (a) Break into cases according to whether x ≤ 0 or x > 0. (b) This is basically automatic everywhere except x = 0 ...
... according to whether x ≤ 1 or x > 1. A lot of the time you can take y = x. 2. The problem is asking you to prove that ∃x∀y : y 2 ≥ x. What number is less than or equal to all squares? 3. (a) Break into cases according to whether x ≤ 0 or x > 0. (b) This is basically automatic everywhere except x = 0 ...
Absolute Value - University of Hawaii Mathematics
... Interval notation allows us to compactly express the shaded region. We list the endpoints, from lest to greatest, or from left to right on the number line. To indicate that we do not wish to include or shade in a particular endpoint, we use the symbols ...
... Interval notation allows us to compactly express the shaded region. We list the endpoints, from lest to greatest, or from left to right on the number line. To indicate that we do not wish to include or shade in a particular endpoint, we use the symbols ...
Lecture 01
... Example: Given a geometric sequence with the first term 2 and a common ratio of 3, which term in the sequence is equal to 192? ...
... Example: Given a geometric sequence with the first term 2 and a common ratio of 3, which term in the sequence is equal to 192? ...
Notes Predicate Logic
... each quantifier applies to the statement to its right. Thus ∀ x, ∃y, P( x, y) asserts that for each x, it is true that there exists a y, which may depend on x, for which P( x, y) is true. On the other hand ∃ x, ∀y, P( x, y) asserts that there is at least one special x for which P( x, y) is true rega ...
... each quantifier applies to the statement to its right. Thus ∀ x, ∃y, P( x, y) asserts that for each x, it is true that there exists a y, which may depend on x, for which P( x, y) is true. On the other hand ∃ x, ∀y, P( x, y) asserts that there is at least one special x for which P( x, y) is true rega ...
