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This collection of solved problems covers elementary and intermediate calculus, and much of advanced calculus. We have aimed at presenting the broadest range of problems that you are likely to encounter—the
Solution: adjusted and transform on a clearer shape. Completing the squares, we rewrite the rst inequality: (a + 1)2+ b. 4 or k(a; b) ( 1; 0)k2 . (a. b) (2; 0)k2 4. The set M can be seen . 4. Similarly, the second inequality means. M = A \ B , where A = U2( 1; 0) a B = U2(2; 0); s, as the intersection of two closed balls. For " >
12 wrz 2019 · 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.
Z 2. 2: (a) Approximate 4cosx dx by the Riemann Sum for f(x) = 4cosx using the right endpoints of 6 equal-sized. 0. subintervals of [0; 2 ]. Z 2. (b) Find the exact value of x2 + 2x dx by calculating the limit of a sequence of Riemann sums. 1.
Water drains out at a rate r(t) L/min. Some values of r(t) are tabulated below. r(t) dt using the midpoint rule on 3 subintervals. (b) Estimate the amount of water remaining in the tank after one hour by approximating the same integral using the Trapezoidal Rule on 6 subintervals.
MATH 138 Calculus 2, Exercises for Chapter 2 1: Evaluate each of the following de nite integrals. (a) Z 3 1 x 3 p x2 1 dx (b) Z ˇ=2 0 cos3 x 1 + sin2 x dx 2: Evaluate each of the following de nite integrals. (a) Z 4 1 lnx p x dx (b) Z 2 0 x2ex=2 dx 3: Find the following inde nite integrals. (a) Z (x2 + 1)exdx (b) Z sin3 xcos2 x dx 4: Evaluate ...
Calculus II Practice Problems 1: Answers 1. Solve for x: a) 6x 362 x Answer. Since 36 62, the equation becomes 6x 62 2 x, so we must have x 2 2 x which has the solution x 4 3. b) ln3 x 5 Answer. If we exponentiate both sides we get x 35 243. c) ln2 x 1 ln2 x 1 ln2 8 Answer. Since the difference of logarithms is the logarithm of the quotient, we ...
