Evaluate the following integral. Students. Instead of the complexity of the problem, working with problems that have small, whole numbers let you zero in on the concepts and principles. Find the radius of convergence of the following power series. 1-cos (theta)/sin (theta) = csc (theta) - cot (theta). The large boxes weigh 55 pounds each, and the small boxes weigh 25 pounds each. Tips and shortcuts are provided to save precious time and effort. sec (theta)/1+tan^2 (theta) = cos (theta), Verify the identity. Reparametrize the curve with respect to the arc length measured from the point where t=0 in the direction of increasing t. r(t)=e^6t cos(6t) i + 6 j+e^6t sin(6t) k. Evaluate the following integral: \displaystyle \int \frac{dx}{(121 + x^2)^2}. Manage your money, stay focused, and get things done. All rights reserved. What is the difference between a number and 20 more than that number? Find the interval of convergence. Find the vectors T, N, and B at the indicated point. Suppose R(t) = (3t^3)i - (2t^2 + 5)j + (4t^3)k. What is the curvature of R(t) if t = 2? Find the solution of the initial value problem y double prime + 2*y prime + 5y = 20e^(-t) cos(2t), y(0) = 10, y prime (0) = 0. Name the test used to determine your answer. Determine whether the vector field F(x,y) = (x+5) i +(6y+5) j is path independent (conservative) or not. Mixed Review is the cumulative practice mode in GMM. The solutions are elaborated with simple, yet detailed explanations. Can't find your question in our library? D. The series diverges 1. sum_n=1^infi... Compute the exact length of the polar curve described by: r = 9e^(-theta) on the interval (9/4)pi less than or equal to theta less than or equal to 6pi. {2(x+5)} / {(x + 5)(x - 2)} = {3(x - 2)} / {(x - 2)(x + 5)} + 10 / {(x + 5)(x - 2)}. (3 * 8) - 2 + (3 + 6) = ? The cable makes a 65-degree angle with the ground. Two times the first number is 12 more than four times the second number. “I don’t believe in the idea that there are a few peculiar people capable of understanding math, and the rest of the world is normal. From an exam perspective, a wide range of questions is covered from a plethora of subjects concepts from Trigonometry and Statistics to Calculus and Integrals. Its maximum speed decreases by 1.3 mph for every inch of snow on the highway. Sometimes, all it takes is a slightly different word choice for a tricky concept to click into place. Find the arc length of the graph of the function over the indicated interval. (cos theta + sin theta)2 = 1 + sin (2 theta), Given cos theta = 3/5 where 0 less theta less pi/2 find: (a) sin (2 theta) (b) cos (2 theta) (c) tan (2 theta) (d) sin (theta/2) (e) cos (theta/2) (f) tan (theta/2), Given tan theta = 12/5 where pi less theta less 3pi/2 find: (a) sin (2 theta) (b) cos (2 theta) (c) tan (2 theta) (d) sin (theta/2) (e) cos (theta/2) (f) tan (theta/2), Find the integral. f(x) = x + 1; [0, 15], Find the interval of convergence of the series \sum_{n=0}^\infty \frac{(x+5)^n}{4^n}, Find curl F for the vector field F = z\sin x i -2x\cos y j +y\tan z k at the point (\pi, 0, \pi/4), Show a separate graph of the constraint lines and the solutions that satisfy each of the following constraints: a. Find the point(s) at which the function f(x) = 2 - x^2 equals its average value on the interval [-6,3] . int_{- 4}^{2} [ int_{pi / 2}^pi (y + y^3 cos x) d x ] d y, Integrate the following. Give the maclaurine expansion. Getting better at math is simple but not easy. Instead of rereading, Karpick found that attempting to retrieve information from memory is the most effective form of studying. P(3, 0, 1), Q(-1, 1, 7), R(6, 3, 0), S(2, 5, 2). f(x, y) = 8y cos(x), 0 less than or equal to x less than or equal to 2pi. A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. Get Geometry Help from Chegg. sum_{n=0}^{infinity} (- 1)^n / (2 n + 1)^2. Find the point on the line y = 2x + 4 that is closest to the point (5, 1). Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 1. Post your questions in the comment box below and we will immediately provide answers and a detailed step-by-step process to solve the same. Consider the vector field F(x, y, z) = (2 z + y) i + (2 z + x) j + (2 y + 2 x) k. a) Find a function f such that F = nabla f and f(0, 0, 0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0,... r(t)=(2 \ln(t^2+1) i+ (\tan^{-1} t) j+8 \sqrt{t^2 + 1} k is the position vector of a particle in space at time t . Let f'(x) = 12e^x + 6 (a) Use indefinite integral to fid f(x). Why is it important for students to talk about math? Sum of (3 + 6^n)/(6^n) from n = 1 to infinity. Consider the vector field F(x,y,z)=(4z+3y) i+(5z+3x) j+(5y+4x) k . A) (3, 3*sqrt(3), 6*sqrt(3)) B) (0, 5, 5), Find velocity and position that has the acceleration a(t)= \langle 3e^t, 18t,2e^{-t} \rangle and specified velocity and position conditions: v(0)=(3,0,-6) \enspace and \enspace r(0)=(6,-1,2). Limit as y approaches 1 of (1/y - 1/1)/(y - 1). All other trademarks and copyrights are the property of their respective owners. Find equations for the following: (a) The plane which passes through the point (0,0,1) which is also orthogonal to the two planes x=2 and y=19. Integral of (du)/(u*sqrt(5 - u^2)). Determine whether the series sum of (2^k)/(k^2) from k = 1 to infinity converges. Estimate f(2.1, 3.8) given f(2, 4) = 2, f_x(2, 4) = 0.4, and f_y(2, 4) = -0.3. Determine whether the series \sum_{n=1}^\infty \frac{(-1)^nn^6}{7^n} converges or not. Who are some modern male mathematicians? a^2z(t - a)\left(\dfrac{1}{z} + \dfrac{1}{a} \right). Find an equation for the plane consisting of all points that are equidistant from the points (7, 0, -2) and (9, 12, 0). Find the point(s) on the surface z^2 = xy + 1 which are closest to the point (7, 8, 0). Use the table of antiderivatives to find 3 x 3 d t. Kim's business earns $10,000 per month. If csc alpha = 3, where 0 less alpha less pi/2, and beta is a Quadrant II angle with tan beta = -7, find cos (alpha + beta).

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