（大一微積分） 請問這題這樣寫正確嗎？背流程寫的😅，圖一為需用到的定義 正確的話，想問紅色圈圈的1是怎麼來的？

DEFINITION Let f be a function defined on some open interval that con- tains the number a, except possibly at a itself. Then we say that the limit of f(x) as x approaches a is L, and we write lim f(x) = L x→a if for every number &> 0 there is a corresponding number 8 >0 such that | ƒ(x) − L| < ɛ if 0 < x-a <8 then

請問34題，沒有想法

microscope, discovering among other things that weevils, fleas, and other 33 creatures come from eggs rather than being spontaneously generated. Not long after this, William Harvey, an English physician, discovered the method 34 which blood circulates in humans and other animals and in 1628 published his findings in the historic treatise “On the Motion of the Heart and Blood in Animals.” 35 , in the 1660s, Isaac Newton discovered the law of gravitation and the laws governing the physics of light, and he also invented differential calculus. > 31. (A) observations (B) descriptions 32. (A) traditional (B) pioneering 33. (A) spineless (B) earthly 34. (A) on (B) to 35. (A) Finally (B) Obviously (C) abstractions (D) generalizations (C) inconsistent (D) falsifiable (C) minute (D) mysterious (C) at (D) by (C) Evidentially (D) Previously

請問這題怎麼解，感謝🙏

- MANUFACTURING At a certain factory, Output Q is related to inputs x and y by the equation y Q = 2x2 + 3x?y2 + (1 + y)3 If the current levels of input are x = 30 and y 20, use calculus to estimate the change in input y that should be made to offset a decrease of 0.8 unit in input x so that output will be maintained at its current level. -

作業寫不出來😭微積分

if (x, y) = (0,0) ( 20 points ) Let f(x, y) = x²y² x4 + y + 0, if (x,y) = (0,0) (a) Does lim f(x,y) exist ? Give reasons. (x,y) → (0,0) (b ) Find the partial derivatives fx(0,0) and fy(0,0).

大一微積分 求求大家幫忙🙏🏻😭

(b ) Find the radius of convergence and interval of convergence of the power series Enzo (-1)n (2x + 3)n 2n

求求各路大神幫幫忙🙏🏻

( 20 points ) Let w = *#y, x=r – 2s +t, y = 2r +s – 3t, z = r2 +52 + . Use the chain rule to find owlər, Ow/as, and Ow/at.

求解答過程

Calculus Quiz 3-1 1. (25%) Determine where the given function 1s increasing and decreasing, and where its graph is concave up and concave down. Find the relative extrema and inflection points, and sketeh the 戰raph of the function. 9 5 x+ 2. (25%) Find the absolute maximum and absolute minimum (if any) 9f the given function on the specified interval._f(x) = 二 守0 3. (25%) Arectangle is inscribed in aright triangle, as shown in the accompanying figure. Ifthe triangle has sides oflength 5, 12, and 13, what are the dimensions ofthe inscribed rectangle of greatest area? 4. (25%) Compute the elasticity of demand for the glven demand function D(p) and determine whether the demand is elastie, inelastic or unit elasticity at the indicated price p.D(p) =一1.3p+ 10;p ==4

力學 救救我 謝謝！（第三題不用）

1. Considerathin rod ofuniform linear mass density pL with mass 4/ and length /, find the gravitational potential。dp/有)。at a perpendicular distance Afrom the center ofthe rod. You may find the integral in (E.6) in Appendix E useful 2. A spherical planet of radius 人> consists ofacore of radius 有/ with uniform density pi. and a thick outer cloud of dust with umiform density p: Find the force (magnitude and direction) onamass箇inside the dust cloud ata position ARp from the planetcenter( 吃<訪<記), 3. Use Fermat's principle by applying calculus of variation to minimize the time oflight passing from medium ofrefractive index jg, to another medium ofrefractive index >, derive the Snells law ofrefraction: js光 名2s 銷 4. Consider the Atwood machine oftwo masses connected by amassless string oflength 7overapulley ofradius gas shown, (a) Write down the total kinetic energy and potential energy in terms of the coordinatex Hence obtain the Lagrangian ofthe system. (b) Derive the Lagrange's equation of motion and hence find the acceleration ofthe masses. x 和二 工

求解 二重積分 已畫出範圍 但無法得出正確答案 會用到Jacobian變數代換嗎？ 謝謝

8. 本valuate the double integral] 二人 二 ] 0 Z2 十 2 和 白9. dZZZ?/ 十 了 1