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

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ಠ_ಠʕ •ᴥ•ʔ 微積分～

Find the indefinlte integraL: Jie 必

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

第17題 謝謝🙏🏻

ms rareempmrrrm 7-22 Evaluate the double integral. 17, 所信計 pisboundedby? 二和 2邦 刀 18. 則 xy224, 5 enclosed by二 生生 is the triangular Tegion With vertices (0, 1), (1,2), (4, 1) 和 世二1 人 0andx 三V1一y is enclosed by the quarter-circle 議守 0, and the axes