Calculus Ii Solved Problems L1 Pdf Solution: we can see the region in question below. x2)2 (x2 1)2 dx. 1. (5 points) write the integral for the volume of the solid of revolution obtained by rotating this region about the line x = 3. do not evaluate the integral. 2. multiple choice: circle the best answer. an improper integral?. Let p(z) = az2 bz c. solutions are: if phas 2 roots: ae r 0x be 1y; if phas 1 root: aer 0x bxer 0x:; if phas 0 roots, then quadratic equation gives complex roots m p d n and solutions are aexp m n x sin p d n x! bexp m n x cos p d n x!. an example of a series: x1 n=0 rn = 1 1 r if jrj<1 and another example: the alternating harmonic.
Exam 2 With Solution Calculus Ii Spring 2011 Math 1020 Docsity Math 1240 calculus ii instructor: richard taylor midterm exam #2 solutions 17 november 2016 11:30{12:45 instructions: 1.read the whole exam before beginning. 2.make sure you have all 5 pages. 3.organization and neatness count. 4.justify your answers. 5.clearly show your work. 6.you may use the backs of pages for calculations. 1. write the most general solution to the di erential equation y00 4y0 4y= 0: 2. which solution ysatisfying y(0) = 1 and y(1) = 0 solves the above di erential equation ? solution. 1. we compute the characteristic polynomial and notice that it factors with a double root: p(z) = z2 4z 4 = (z 2)2: so the general solution is y= ae 2x bxe 2x: 2. Math 152 – calculus ii midterm examination 2 solution set department of mathematics fall term 2012‐2013 – december 20, 2012 fair use disclaimer, this document contains copyrighted material. we are making such a material available in our. Math 141 { calculus ii second midterm exam solutions (1) (a) a right triangle with angle , opposite side length p 2 and adjacent side length 1 satis es tan = p 2. since the hypotenuse has length p 3 = q 12 (p 2)2, cos = 1= p 3. (b) f0(x) = 3=x4 3 <0, so by the mean value theorem fmust be one to one. (c) notice that f 1( 2) = 1. hence, (f 1)0.
Solutions To Quiz 2 Problems Calculus Ii Math 129 Docsity There are 6 problems on this exam; problems 3 and 6 have multiple parts. there are 7 pages to the exam, including this page; all are single sided. check to see if any are missing. do your work in the space provided in this booklet. use the back of pages if you need more room. scientific calculators are allowed. no books or notes are allowed. Circle the letter of the best answer. make sure your circles include just one letter. these problems will be marked as correct or incorrect; no partial credit will be awarded for problems in this section. (20 points) evaluate the integrals. (11 points) evaluate the improper integral if it converges. Math 1240 { midterm exam #2 (solutions) 28 march 2019 5 problem 5: a 16m deep diving pool is made by revolving the graph of y= x2 (0 x 4) about the y axis. the pool is full of water. how much work does is take to pump out all the water to the level of the top of the tank? express your answer in terms of the density of water, ˆ, and the. The sample tests are just to give you an idea of the a general idea of the topics covered, the level of difficulty, how questions may be worded and, if solutions are provided, what is the acceptable level of detail required in the solutions. this page maintained by robert sharpley ([email protected]) and last updated february 9, 2005.
Calculus 2 Chapter 2 Pdf Math 1240 { midterm exam #2 (solutions) 28 march 2019 5 problem 5: a 16m deep diving pool is made by revolving the graph of y= x2 (0 x 4) about the y axis. the pool is full of water. how much work does is take to pump out all the water to the level of the top of the tank? express your answer in terms of the density of water, ˆ, and the. The sample tests are just to give you an idea of the a general idea of the topics covered, the level of difficulty, how questions may be worded and, if solutions are provided, what is the acceptable level of detail required in the solutions. this page maintained by robert sharpley ([email protected]) and last updated february 9, 2005.
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