多様体の接ベクトルに関する性質の証明なんですけど、(1)が分かりません。 素直に訳すと、(1)は「多様体上の滑らかな関数fとgが点pの座標近傍で同じなら、その接ベクトルv(f)とv(g)は同じになる」だと思うんですけど、証明でf(p)=0,g(p)=1と明らかに異なる値をと... 続きを読む

11. Lemma. Let ve T,(M). (1) If f, ge F(M) are equal on a neighbor- hood of p, then Uf) = v(g). (2) If he F(M) is constant on a neighborhood of p, then u(h) 0. 三 Proof.(1) By linearity it suffices to show that if f = 0 on a neighbor- hood W of p, then u(f) = 0. Let g be a bump function at p with support in W; then fg = 0onall of M. But v(0)= u(0 + 0) = u(0) + u(0) implies v(0) = 0. Thus 0= (fg) = v(S)g(p) + f(p)v{g) = u(f), since f(p) (2) By(1) we can assume that h has constant value c on all of M. If 1 is the constant function of value 1, then 0 and g(p) 1. ニ (1) = (1.1) = (1)1 + lu(1) = 2v(1). Hence v(1) = 0, and v(h) = u(c· 1) = cu{1) = 0.

問題の解き方や、答えが分からないです。また、問題を解くために高校数学や大学数学のどの単元の知識が使われているのかも合わせて教えて頂きたいです。よろしくお願いします。

問(i)~(vi) に答えよ。 解答は解答用紙の所定欄に日本語で記すこと。 導出過程も簡潔に記す こと。 Let the function f(n) be defined as S(n) = cos? where n and 入 are positive integers (greater than 0). (i) Assuming n>1000 and 42 < 76, determine f(n). (i) Assuming is a prime number, determine the smallest n such that 『(n) = cos? %D

上の式から下の式への式変形で、明らかに両辺に−1をかけていますよね？なのにどうして不等号の向きが変わらないんですか？ https://hiraocafe.com/note/trigonometric-inequalities.html#link3 URLの数Ⅰ三角比の練習... 続きを読む

2(1 - sin?0) - (2 - V3) sin 0 - 2+ V3<0 2 sin' 0+ (2 - V3) sin 0 - V3 <0

一番目が問題で二問目が答えなんでがわかる方教えください

EVALUATING FUNCTIONS The symbol f(x) represents the real number in the range of the function f corresponding to the domain value x. Symbolically, f:x→f(x). The ordered pair (x, S(x)) belongs to the function f. Ifxisa real number that is not in the domain of f, then fis not defined at x and f(x) does not exist. Examples: 15 a) Find f(6), S(a), and f(6+a) for f(x) 三 3° X - b) Find g(7), g(h), and g(7+h) for g(x) = 16+ 3x x. 2 Find k(9), 4k(a), and k(4a) for k(x) Vx c) 2 For the above functions, determine the resulting domain. Solutions: a) b) c)

一番目が問題で二問目が答えなんでがわかる方教えください

EVALUATING FUNCTIONS The symbol f(x) represents the real number in the range of the function f corresponding to the domain value x. Symbolically, f:x→f(x). The ordered pair (x, S(x)) belongs to the function f. Ifxisa real number that is not in the domain of f, then fis not defined at x and f(x) does not exist. Examples: 15 a) Find f(6), S(a), and f(6+a) for f(x) 三 3° X - b) Find g(7), g(h), and g(7+h) for g(x) = 16+ 3x x. 2 Find k(9), 4k(a), and k(4a) for k(x) Vx c) 2 For the above functions, determine the resulting domain. Solutions: a) b) c)

一枚目が問題で二番目が答えなんですがわかる方教えください。

EVALUATING FUNCTIONS The symbol f(x) represents the real number in the range of the function f corresponding to the domain value x. Symbolically, f:x →S(x). The ordered pair (x, (x)) belongs to the function f. If xisa real number that is not in the domain of f, then fis not defined at x and f(x) does not exist. Examples: 15 a) Find f(6), f(a), and f(6+a) for f(x) X - 3° b) Find g(7), g(h), and g(7+h) for g(x) = 16+ 3x x. 2 c) Find k(9), 4k(a), and k(4a) for k(x) = 2 For the above functions, determine the resulting domain. Solutions: a) b) c)

英語と数学わかる方教えください！

EVALUATING FUNCTIONS The symbol f(x) represents the real number in the range of the function f corresponding to the domain value x. Symbolically, f:x → f(x). The ordered pair (x, S(x)) belongs to the function f. If xis a real number that is not in the domain of f, then fis not defined at x and f(x) does not exist. Examples: 15 a) Find f(6), S(a), and f(6+a) for f(x) x -3 b) Find g(7), g(h), and g(7+h) for g(x) 16+ 3x - x. 2 Find k(9), 4k(a), and k(4a) for k(x) Vx 2 For the above functions, determine the resulting domain. Solutions: a) b) c)

英語と数学わかる方教えください！

EVALUATING FUNCTIONS The symbol f(x) represents the real number in the range of the function f corresponding to the domain value x. Symbolically, f:x → f(x). The ordered pair (x, S(x)) belongs to the function f. If xis a real number that is not in the domain of f, then fis not defined at x and f(x) does not exist. Examples: 15 a) Find f(6), S(a), and f(6+a) for f(x) x -3 b) Find g(7), g(h), and g(7+h) for g(x) 16+ 3x - x. 2 Find k(9), 4k(a), and k(4a) for k(x) Vx 2 For the above functions, determine the resulting domain. Solutions: a) b) c)

数学苦手な上英語なのでよくわかりませんがわかる方いらっしゃたら教えください

EVALUATING FUNCTIONS The symbol f(x) represents the real number in the range of the function fcorresponding to the domain value x. Symbolically, f:x → S(x). The ordered pair (x, f(x)) belongs to the function f. If xis areal number that is not in the domain of f, then fis not defined at x and f(x) does not exist. Examples: 15 a) Find f(6), f(a), and f(6+a) for f(x) x -3 b) Find g(7), g(h), and g(7+h) for g(x) = 16+ 3x - x。 2 c) Find k(9), 4k(a), and k(4a) for k(x) = 2 For the above functions, determine the resulting domain. Solutions: a) b) c)

(I)が関数で(ii)が関数じゃないらしいのですが何故か教え欲しいです

Determine whether each set specifies a function. If it does, then state the domain and range. 2) i) S = {(I1,4), (2,3), (3,2), (4,3), (5,4)} T= {(1,4), (2,3), (3,2), (2,4), (1,5)} Solutions: i) Prepared by DZ Page 3