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# Calculus II MATH 1220

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This 4 page Class Notes was uploaded by Miss Noel Mertz on Monday October 26, 2015. The Class Notes belongs to MATH 1220 at University of Utah taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/229930/math-1220-university-of-utah in Mathematics (M) at University of Utah.

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Date Created: 10/26/15

Review problemsExam1 MATH 12207 Spring 2005 zxz 1 1 71 Calculate D75 ln ln 13 dx 2 71Calculate 1 z 1 3 71Calculate0 m dz 4 W2 For xz 71 nd f 1z and verify that z and z 5 73 Calculate D75 exz nx 6 73 Calculate zexz1 dz 7 WA Calculate D75 log2z3 1 8 WA Calculate D75 23 312 9 WA Calculate D75 12 11quot 10 75 A radioactive substance has a halflife of 800 years If there were 10 grams initially7 how much would be after 150 years Deduce the equation of the exponential decay 11 76 Solve the differential equation zy 1 zy 6 y 0 when I 1 12 76 A tank initially contains 100 gallons of brine with 25 pounds of salt solution Brine containing 1 pound of salt per gallon is entering the tank at the rate of 2 gallons per minute and is owing out at the same rate If the mixture in the tank is kept uniform by constant stirring7 nd the amount of salt in the tank at any time t 2 13 77 Calculate D75 lt1 tan 1 14 WY Show the identity tansin 1 z cosh dz 15 WE Calculate 16 81 Calculate dz 1 17 81 Calculate dz 18 82 Calculate sin32zcos2z dz 19 82 Calculate sinzcos2z dz 1 t 20 83Cl lt idt ltgtlt gt 3m 2z1 21 83 Which trigonometric substitution is used in order to compute the integral dz 7 Write V12 4x 5 the integral with the new variable 22 84 Calculate ln74 dz 23 84 Calculate 12 T dz E0 5 HH H53590071 Haas mews H 533 Math 1220 1 Review 3 Expand I4 7 313 212 z 7 2 in a Taylor polynomial of order 4 based at 1 Find the thirdorder Maclaurin polynomial for l z32i 1 Use the trapezoidal rule with n 10 to approximate cossin z dzi 0 7r Use Simpon7s rule with n 6 to approximate sinz dzi 0 Approximate the real root of 713 z 7 5 0 using Newton7s Method to ve decimal places i Approximate the real root of 2 cosz 7 6 0 to two decimal places by using the Bisection Method on 1 2 Find the standard equation of the parabola with vertex at the origin and directrix y Find the equation of the ellipse with a focus at 03 and minor diameter 8 Find the equation of the hyperbola with focus at 50 and vertex at 30 Sketch a design for a re ecting telescope that uses a parabola and an ellipse i If a planet orbits a star in an elliptical path and the star is located at 500 and the planet is measured to be 150 million miles from the star when the angle from the origin to the star to the planet is 135 degrees give the equation of the planets orbit assuming the star is at one focus and the center of the ellipse is the origin Find the Cartesian equation of 7 2 7 8T cos 9 12T sint9 0i i Graph T 2cos 39 i Graph T 29 for 9 2 0 Sketch the following graphs and give their points of intersection 7 2 4cos2t9T 2 sint9 Sketch one leaf of the rose T 3 cos 29 and nd the area of the region enclosed by it Find the area of the region outside the circle T sint and inside the cardioid T l cos 9 H to 9 0 F 533 7 9 HHH MHOSO H CA3 HH mi H on H H H 00 H 50 to O i Solve the following differential equation i Prove that sintan 1z 1 Math 12201 Test 1 Review Find D ln12 7 51 i Find D75 61 Find D75 Find D75 3212731 i Use logarithmic differentiation to nd Dml12 3II 7 71 Findmdzi Findzexzigdzi Find 1057 1 din Find f 12 sin I dzi i Find fsin2zdzi i Find f zsin12 7 4 dzi i Find 6 sinzdzi dz kzy where k is some constant i Solve the following differential equation y 7 12y 312i i Give an example of a strictly monotonic functioni Why are these functions usefu i If I5 13 7 2 what is f 107 and when is f 1 differentiable 11 xz2212i i Findtx16t2dti Find zz 7 1 dzi iFinddz 77I22 15731271 21 Flndmdz 2 22 Find I 3 d 1372z2172 I

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