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We will derive formulas to convert between cylindrical coordinates and spherical coordinates as well as between Cartesian and spherical coordinates (the more useful of the two). Here is a set of practice problems to accompany the notes for Paul Dawkins Calculus II course at Lamar University.
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Evaluate each of the following integrals. Here is a set of practice problems to accompany the Integration by Parts section of the Applications of Integrals chapter of the notes for Paul Dawkins Calculus II course at Lamar University.
Practice problems for calculus II. Problems are given which require some basic techniques. 1. Find the antiderivative of xln(3x) 2. Find 2 ¢ (x2 ¡ 8x + 15)¡1dx. 3. Find sin7(t)cos3(t)dt. Determine if the following converge, and if they do, compute them.
The Calculus 2 Practice Tests cover all the main concepts of calculus, including derivatives, Euler’s method, integrals, Lagrange error, L'Hopital's rule, limits, parametric, polar, Taylor and Maclaurin series, and vectors.
Problem Set: Moments and Centers of Mass. Problem Set: Integrals, Exponential Functions, and Logarithms. Problem Set: Exponential Growth and Decay. Problem Set: Calculus of the Hyperbolic Functions. Module 2 Review Problems.
SOLUTIONS. Please answer all of the questions, and show your work. You must explain your answers to get credit. You will be graded on the clarity of your exposition! Date: December 12, 2018. Consider the region bounded by the graphs of f (x) = x2 + 1 and g(x) = 3 x2.
Calc II: Practice Final Exam 4 Part II. Sequences and Numerical series. 1. Determine whether the sequence converges or diverges. If it con-verges, nd the limit. (a) an= nsin(2=n) It converges to 2, using L’Hopital (lim x!0 sin2x x = 2:) (b) an= 2n=n! 0 <an 4=n!0; hence an converges to 0 by the squeeze theorem. 2.
Calculus II Final Exam Practice Problems. (a) Sketch the conic section. Find and label any foci, vertices, and asymptotes. ( x − 3 ) 2 − 9 y 2 = 36. (b) Find the equation of the ellipse with foci (0, 2) and semi-major axis length 3. (a) Find the area of one petal of the rose r = 4sin(3 ).
For the following exercises (1-2), determine the area of the region between the two curves in the given figure by integrating over the [latex]x\text{-axis}\text{.}[/latex]