MAT135H1 Lecture 10: Lecture 9-10

QQ浏览器 文件 编辑 显示 历史记录 书签 窗口 帮助 wski, Colin Adams å‡¸å®‰å ¨ ã€‚å¯¼å ¥ä¹¦ç­¾ https://artsc media case.edu/ p-content/uploads/sites 116/2015/11 15005409 Math 121 Final review.pdf 凸应用中心 Math-121-Final-review.pdf 4 22 time when r- meat 2min In Problems 100 to 103, given f(x), find g'(b) where g(x) is the inverse of f(x) m ladder sli the height of th 100. f(x) -3x wall to the 4 b-3 102. f(x) x-1 ax.tcrlt th 101. f(x)-3+1 b 2 ng down the 104. Find the equation of the tangent line to f(x)-21 at the point where 3 e toplids d105. Find the equation of the tangent line to y -e2^ In(2x) at a-2 h and x at the n 106. Find the equation of the tangent line to f(x) 07. Find the equation of the tangent line to y- 1x3 + 6x at the point (2, 18) -2r2 at (1,-1) and radius 2 m a s te 51 Exercise 13, but 108. Find the values of x for all points on the graph of f(x)-z?一2x2 + 5x-16 at which the slo in when it is 2 m tangent line is 4 109. Find the point(s) on the graph of y r2 where the tangent line passes through the po+, (2 14

(1 pt) Let V-p? For (u,12), (v1, U2) E V and a E R define vector addition by (u 1 , u2沺(V1Mz) := (u1 + U1+ 2, u2 + ข2-1 and scalar multiplication by a (m ,u2) :-(aul t. 2a-2, au2-a + 1). It can be shown that (V,田,U丬is a vector space over the scalar field R. Find the following yY on the sum: (-6,8) H (3,0) 1 the scalar multiple: 1 (-6,8)--6 the zero vector 0 the additive inverse of (x, y) (z, y) ( -2-x -y

2. Find the integral 1 of the function F(a, y, 2) -1- z over the graph of the function hr.) 3. Find the average valuo of 4. A metallic surface S is in the shape of a hemisphere z- VR-y2, where (x, y) satisfies 2 with 2S 1. the function f(z, y, z) ao +r +2 on the curve C parameterized as e(t) = (cos t, sin t,t), 0 st 21. %2,2+y2 . A2, and it has the mass density 6(nzuz)三Z2+ 1,2. Find the centre of gravity of s. Find the surface integral I C