Consider the following functions. f(x) = 4 sin x g(x) = 4 cos 2x Sketch the region bounded by the graphs of the equations. y y -4- y y Find the area of the region. (Round your answer to three decimal places.) 六12 KIO KIN

Q: Find div F and curl F if F(x, y, z) = 10e"Y i – cos yj+ 8 sin? z k. div F= curl F=

A:

Q: Calculate the following derivative. (Use symbolic notation and fractions where needed.) d (15 Vsin…

A:

Q: Calculate D(fog) for the functions f(x, y, z) (st, tu, su).

A: answer is in next step

Q: S (In 2x2 dx

A: Evaluate the integral :    ∫ln 2x2 dx

Q: f" (x) = cos x, f(0) = 1, f'(0) = 2, f'"(0) = 3.

A:

Q: Describe the graph of the equation. r = (5 – 31) i – 81 j O It is a line in 2-space that goes…

A: Given : r=(5-3t)i-8tj

Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

A:

Q: 5 S Ix² x- 6|dx -5

A: The given integral,            ∫-55x2-x-6dx

Q: Use the Comparison or the Limit Comparison test to show convergence or divergence of each series.

A: Explained below

Q: Find the particular solution of the differential equation that satisfies the initial condition(s)…

A: topic - differential equation

Q: Sketch the region enclosed by the curves and find its area. у %3 сos 9x, y —D 0, х - x = 18' 9 NOTE:…

A:

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Given points,  P(0,0,0), Q(4,2,4)

Q: n2-2

A: Question number 5 is solved step by step. Solving more than 1 question is against the policy of…

Q: Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

A:

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere x² + y?…

A:

Q: Find curl (4z i + 5x j + 3y k). Exact number, no tolerance. curl (4z i + 5x j+ 3y k) = (i )i + ( )j…

A:

Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables æ, y, z)…

A: Given problem:-

Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

A:

Q: Determine the work done by the constant force. The locomotive of a freight train pulls its cars with…

A: Given data÷

Q: Determinant of 2 x 2 Matrices. Solve for the determinant of the following matrices: [7 -3] A = 4 6 B…

A: We know that for a matrix A=abcd=ad-bcA=7-346=7*6-(-3*4)                       =42+12…

Q: 8. 1) Use the Integral Test to determine whether the series is convergent or dive n' +1 n=1 Please…

A:

Q: Use double integration to find the volume of the solid bounded by the paraboloid 2 = 9X- + y, below…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: Consider the piecewise-defined function Jr+3, |1- x, x 0. (a) FUNCTION, so it must pass the…

A:

Q: Use the graph of the function f to decide whether the value of the given quantity exists. (If an…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: Improper integral: If f(x) is not continuous at x=c where a<c<b and ∫ac f(x) dx and ∫cb f(x)…

Q: Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t…

A:

Q: -4 = ニ 200

A: To solve for x using the the given equation.

Q: Given that f'(x) is continuous everywhere and changes from negative to positive at x=a, which of the…

A:

Q: (x + 1) f' (x) = f(1) = 5 x,

A: Solution is given below:

Q: Find the area of the region bounded by the graphs of f (x) = x° and g (x) = Xx. A 1 в) 4 0.5 D 3

A:

Q: ||r(t) × r"(t)|| ||r'(t)||* Use the formula k(t) : to find k(t). r(t) = e"i+ ej K(t) :

A:

Q: Point Func tion h(x.y)-7ycos (x-y) Co,Ti/3) Dn(o,1/3) = %3D

A:

Q: A. Sketch the figure for analysis. Shade the needed region and draw a representative vertical or…

A: Here, the region is bounded by the curves: x=4, y2=x

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A:

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A:

Q: Find V · (V × F), if F(x, y, z) = e2²i+ 7xe'j – 2e²k. - V·(V × F) =

A: Solved below

Q: Find the area of the region enclosed by the curves y = x² and y integrating with respect to y. = 6x…

A:

Q: Evaluate the given integral by changing to polar coordinates.     sin(x2 + y2) dA   R, where R is…

A:

Q: Find f-(-1,1) of the function: f(x, y) = x + xy +2a°y?

A: Let's find.

Q: AX = B is a matrixial representation of a lineal system of equations. Over the augmented matrix (…

A: Here we have to choose the correct option.

Q: Find div F and curl F if F(x,y, z) = x*i – 7j + yzk. - div F= curl F=

A:

Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi + yj – zk. | V · (F x G) =

A:

Q: an

A:

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

A: To find unit tangent vector at given parameter.

Q: Find the general solution: y" + 4y' + 6y = 0.

A:

Q: H.W (5) Solve the following differential equations of (x'+y')dx+(2xy cos y)dy phee

A:

Q: im Y cosx tZx 7x¢ with squeze thearem

A:

Q: (a²- x²}3½ dx

A: see below the answer and calculation

Q: n/2 c sine Evaluate the iterated integrals J. r cos e dr de 0. A 1/6 B 1/2 c) 6 D) 11/9

A: