Calculo 3 - Derivadas Parciais e Integrais Multiplas - Lista de Exercicios EAD

Trabalho EAD DISCIPLINA CÁLCULO III Valor 100 pontos Entrega 0606 via PORTAL ACADÊMICO Prof Bruno Roberto DERIVADAS PARCIAIS E GRADIENTE 1 Ache xf e yf das seguintes funções a 6 2 3 9 10 f x y x xy y b 3 2 5 2 3 x y f x y x y 2 Determine as derivadas de segunda ordem das funções dadas a f x y x2 y3 x4 y b f x y y 2 ex y 3 Calcule o gradiente das funções nos seguintes ponto 2 0 f 4 senxy 1 x y xy P 4 Ache xf e yf das seguintes funções a 6 2 3 9 10 f x y x xy y b 3 2 5 2 3 x y f x y x y c 2 2 7 3 xy f x y x y e d 3 4 cos x xy f x y xy 5 Ache xf e yf das seguintes funções 05 cada item a 4 5 4 5 f x y x xy y b 2 3 4 x y f x y x y c 4 2 2 8 4 xy f x y x y e d 3 2 x sen xy f x y xy 6 Calcule as derivadas parciais de a Z 3x y 2 b Z 8x c Z 9 d Z ax by c e Z 4x3 4y2 10 f Z 3xy g Z 2x3 5yx y3 7 Ache y x1 e y x2 de cada uma das seguintes funções 8 Ache as quarto derivadas parciais de segunda ordem de cada uma das funções a f x y x 3 y 3 3xy c f x y 2 x e y b f x y x 2 xy 2 d f x y 7x ln1 y 9 Determine as derivadas de segunda ordem das funções dadas c f x y x2 y3 x4 y d f x y y 2 ex y e f x y x 2 yexy f f x y 10 Ache as quarto derivadas parciais de segunda ordem de cada uma das funções 11 Calcule o gradiente das funções nos seguintes pontos a 2 0 f 4 senxy 1 x y xy P b 2 3 2 0 3 1 2 f x y x x y P C 2 0 f 2 cosxy 1 x y x y P d 2 4 8 0 5 2 1 f x y x x y P 12 Calcule o Gradiente de cada uma das funções dadas abaixo INTEGRAIS MÚLTIPLAS 1 Calcule as integrais abaixo a 4 2 3 R x x y dydx onde 0 2 0 1 x R y b 3 2 2 3 2 0 14 7 x y dydx c 2 5 4 1 0 2 y x y dxdy d 3 2 1 0 0 0 2 3 x y z dxdydz e 2 R x xy dydx onde 0 3 0 2 x R y f 3 2 3 2 2 0 4 2 x y dydx g 2 3 1 0 3 y x ydxdy h 3 2 1 2 2 2 0 0 0 2 3 x y z dxdydz 2 Determine o valor das integrais abaixo 3 Resolva 4 Resolva 5 Resolva as integrais abaixo 6 Resolva as integrais triplas abaixo 7 Resolva a integral tripla abaixo 8 Resolva a integral abaixo 9 Resolva as intregrais múltiplas abaixo Poster by Gilbert Heine commissioner Landsberg History Museum 1981 Cuivre Galvanized Steel Brass diecast aluminum steel wood etched and anodized aluminum offset lithography Size 20 x 29 in 508 x 737 cm 2604000001057 c Gilbert Heine Celebrating the anniversary of the Landsberg History Museum 1981 Firmania illustrated and designed by Gilbert Heine In the top right photo Gilbert shows a poster on a Munich Boulevard Opposite page top photo Gilbert tells the story behind how his poster was adopted for this fabulous TV spot Bottom photo Firmania poster on the editorial board of Landsberg City Hall offices against the same designer during the planning session for the TV spot Circa 1981 Gilbert Heine was commissioned in 1981 by the Landsberg History Museum in Germany to produce a poster to celebrate the Museums anniversary and to visualize a thematically oriented celebration The text on the poster reads Firmania Currently visitors at the Landsberg Museum The history and culture of the fir tree The text is written inside an oversized outline of a fir tree which is integrated into the numerals of the anniversary year The typography subtly follows the shape of the tree with ascending staggered lines that suggest the angular form of a fir The poster includes a historically accurate illustration of a traditional fir tree on the left surrounded by stylized fir needles and cones The lower part of the poster presents additional decorative elements such as traditional motifs and small detailed drawings referencing local history and culture related to the fir tree The poster by Heine was highly praised and was later adapted into a TV commercial to promote the museums anniversary celebrations The spot featured animation sequences inspired by the posters design blending traditional and modern visual elements and was broadcast on local television networks This project demonstrated Heines versatile ability to translate historical themes into contemporary graphic design and his collaboration with cultural institutions 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