ZzJm 3. Use integral test to determine whether the series 4. Use an appropriate test to determine whether the series 11-1 converges or diverges. n²(n+1)! n!22 is convergent or divergent.

Q: Find the arc length of the parametric curve. x = 24 cos(t), y = 24 sin(t), z = 7t; 0<t< T L =|25

A:

Q: Let f(x) = 2x³-7x² + 4x. a. On what interval(s) is f'(x) > 0? b. On what interval(s) is f(x)…

A: Given problem:- Let f(x) = 2x3 - 7x2 + 4x .   a. On what interval(s) is f'(x) &gt; 0?   b. On what…

Q: Find the four second-order partial derivatives for f(x, y) = 8x5y³ +5x6y7.

A:

Q: Find the area that the curve encloses and then sketch it. r = 11(1 + cos ?)

A:

Q: 2. Find the area of the region bounded by the curve r = 2 cos 30 .

A: Given problem:- Find the area of the region bounded by the curve r = 2cos(3θ)

Q: Find the exact length of the polar curve. r = e4?,    0 ≤ ? ≤ 2?

A:

Q: Begin with the Maclaurin (Taylor) series: cos r = 1 - 2! 4! 6! (a) Evaluate cos 0. (b) List the…

A: According to the guidelines, we are instructed to answer 1 question or 3 sub question,the others can…

Q: 6. A parallelogram is defined by the vectors (4, 3) and (1, 2). Determine the perimeter of the…

A: The parallelogram is defined by the vectors (4,3) and (1,2)  We have to determine the perimeter of…

Q: 7. Evaluate (5 – x)dA where R {(x, y) : 0 < x < 5,0 < y < 3}

A: Double integral

Q: Use a parametri. tion to express the area of tne surface as a double Integrai. Then The portion of…

A:

Q: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

A: A)P(x)=R(x)-C(x)       =5x -(0.003x2+1.4x+60)P(x)=3.6x-0.003 x2-60b)R(50)=5(50)…

Q: Use Newton's method to approximate a root of the equation z + c + 3 - 0 as follows. Let I, = -1 be…

A: Let's find.

Q: Do not use a calculator for this problem. Find the x-value where the relative maximum of y closest…

A:

Q: n 9 = k=1 Note: Your answer should be in terms of n.

A: Solve the given

Q: Investigate the given two parameter family of functions. Assume that a and b are positive. f) =…

A: We will plug the values of a and b to do the analysis.

Q: Given that the vectors X1 = () e- -2t ,X1 = (C)e-6t are solutions of a system x' = AX, do they form…

A:

Q: Let z = g (x, y) = x³ + xy³ + y4 - 6x - 2y + 4, where x = r cos (0) and y дz Use the chain rule to…

A: We will use chain rule to find the derivative

Q: 6 Select the conic section represented by the equation. 5x 2 + 5y 2 = 0 point hyperbola  line…

A:

Q: Find the equation of the tangent line to the function y = xsin x when x = 6.

A:

Q: Find the curvature and the radius of curvature at the point t = 0. x = e cos(t), y = et sin(t), z =…

A:

Q: Solve the following: 1. Create a table, a verbal description, and a piecewise function to represent…

A:

Q: Problem 4. Part (a) Part (b) 5ln(3-x) = 4 Do both parts. Write the sum using sigma notation:…

A:

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A:

Q: -3x+1) -3х 2-3* dx

A: According to our company policy we are supposed to answer only first question and rest can be…

Q: In the triangle below, BA=u and BF=v. Express each of the following in terms of u and v. a) CD b)…

A:

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Height is given by f(t)f(t)=-16t2+420t+6t =11.5

Q: The Cartesian equation of the straight line tangent to the plane curve given parametrically by the…

A: This question can be solved using the concept of tangent and normal under application of…

Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx

A:

Q: Current Attempt in Progress Evaluate the definite integral. e i + e='j+t k )dt

A:

Q: Find and classify the critical points of f(z) = 82°(8 - z)7 as local maxima and minima. %3D Critical…

A: Critical points are the points of a function where the derivative does not exist. local maxima: the…

Q: For a, b E R, calculate (ax + b)dx (x²+1)²(x²+4)*

A:

Q: Determine the position function if the acceleration function is a(t) = 6sin t+5, the initial…

A:

Q: A rectangular swimming pool is 20.0 ft wide and 50.0 ft long. The bottom slopes evenly (lengthwise)…

A:

Q: analyze and trace the given curves y = x2 + 1 / x2

A: Explained below

Q: Given the relation x³z² + sin(3z - 2y) - 8√9+7x³ + 5y + 13 = 0 implicitly defines y as a…

A: Differentiate

Q: The following is a graph of y = f(x) A= (0,8) You Select the correct graph for the following…

A: We have to find out the graph

Q: Consider the space curve r(t) = (cost cos 2t, cost sin 2t, sin t). (a) Find r(t).

A:

Q: n k=1 Note: Your answer should be in terms of n.

A:

Q: 304² 3x Evaluate dx dy, by first Reversing the order of integrals. √36 + x3 Enter an integer or a…

A:

Q: Consider the following. Let u = 4x³ - 1. Find du. du = dx Indicate how the limits of integration…

A: The given definite integral,          ∫01x24x3-14dx

Q: Evaluate the definite integral. 12 dx 25 + 2x 2

A:

Q: What is wrong with the equation? -5 15 dx = -4 64 -2 f(x) = x-5 is not continuous at x = -2, so FTC2…

A:

Q: Use Green's Theorem to evaluate the line integral [xy dx + ( xy dx + (x² + x) dy where C is the path…

A:

Q: The eigenvalues of the matrix 139 - 84 240 145 (a) Find an eigenvector corresponding to X₁ = 1 X1 =…

A:

Q: ^ du 1 1+2 Sinn

A: Solving the given integral using the substitution method Also using the formula for the integration…

Q: The velocity of a particle in space at time t is given by(t) = 2t² i + 2t k Find the distance…

A:

Q: 15 17 23 28 ? 40 28 8 3 12 13 2.

A: Consider

Q: Let the graph below represent an object's velocity as moves away from a sensor. At what time, in…

A: This integration can also be found from area under the curve .

Q: 5. y = 2 sin x y

A:

Q: 7. y=2 cos(x) - 1 끌 3m

A: