Use the divergence theorem to calculate the surface integral F. dS; that is, calculate the flux of F across S. F(x, y z) = x?zi + xz³j + y In(x + 1) k, S is the surface of the solid bounded by the planes x + 2z = 8, y = 6. x = 0 y = 0, and z = 0 x + 2z = 8 y = 6

Q: 1. The sum of the digits of a two digit number is 15. One-third of the number diminished by 12 is…

A: A detailed solution is given below.

Q: 19. e dr

A: Topic = Integration As per guidelines , At a time only one question can be answered. please repost…

Q: The integral TT tan x sec?x dx is an improper integral of type I that diverges is an improper…

A: To evaluate the following integral.∫π2π tan x sec2 x dx

Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: INTRODUCTION TO MATRICES Answer the following questions: Given the Matrix A below. 3 12 21 A- 17 15…

A: This is a problem related to matrix . Based on the general formula and concepts we will answer the…

Q: r3 5x-2 5.) . V5x+1 xp!

A: This is a problem of integration. Based on the general formula and concept we will answer the…

Q: #1 Evaluate F• dr. F(x, у) — хі + уј C: r(t) = (9t + 2)i + tj, 0sts1

A:

Q: Question 7 Use cylindrical shells to find the volume of the solid generated when the region enclosed…

A:

Q: Find V · (V × F), if F(x, y, z) = 2e"²i+ 2xe"j – 9ev²k. V· (V × F) =

A: Given F(x,y,z)=2exzi→+2xeyj→-9eyzk→ To find, ∇.(∇×F)

Q: Question 6 Find the area, A, of the region enclosed by the cardioid r = 8 + 8 cos 0. 48 n 96 n 52 n…

A:

Q: Find the curvature and the radius of curvature at the stated point. Edit r(t) = 8 cos(t)i+ 7 sin(t)j…

A:

Q: Find V · (V × F), if F(x, y, z) = 5e²i+ 5xe®j– 7ev²k. %3D V ·(V × F) =

A: We know divergence of curl of any vector v is always zero.

Q: 524–121x4 lim x00 62xº+24x4+234x³+11x2+169 ||

A:

Q: Given the function f(x) = Which f the following is/are true? (x- 1)(x + 1) 1. lim f(x) = +00 2-1+ 2.…

A:

Q: Hi there, please help me with answering this question. I am a bit confused here. It would be highly…

A:

Q: Find div F and curl F if F(r, y, z) = 2e*"i– 9cos yj+ 4 sin² z k. div F= curl F=

A: Given: F(x,y,z)=2exyi-9cosyj+4sin2zk

Q: 3) Find and d²y of the following equation then simplify whenever possible. dx dx² x = 3em y = 2mem

A: A detailed solution is given below

Q: 2. lim (e* – 1)lnx X0+

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: greens theorem

Q: Determine the vector field of F. F(x, y) = yl – x) 1.

A: Vector field

Q: Find dy/dx for the following a. e2y+x3=y b. In(3xy) = x+x⁵

A:

Q: y" + 2y' + 5y = 3 sin(2t)

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t→+∞\ 5t2 +6' 8t (?, ?)

A: To evaluate the following limit.limt→+∞t2+85t2+6, 18t=?, ?

Q: 4. Using logarithmic differentiation, or otherwise, find the derivative of y = (sin r)".

A:

Q: Find the volume of the solid generated when the region enclosed by the given curves is revolved…

A: Plotting given curves on the graph

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

A:

Q: Evaluate the line integral -ydr + rdy along the curve C : y² = 6x from (6, 6) to (0,0). NOTE: Enter…

A:

Q: Evaluate each integral. dr 1. VI² – 1 2. [zcos I Cos az dz 7x +1 dr 2-- 2 3. 7 – I – z

A:

Q: Q6 Find dy, if y= +++

A:

Q: dy_ y -1 dx

A:

Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 5xyz k. V × (V × F) :

A:

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Here,  0≤x≤4-yy≤z≤8-y0≤y≤4 To change the order of integration to dx dz dy to dz dy dx

Q: (2a+1)(x–2) lim x00 (3x-1)(x+2

A: Given query is to find the limit of the expression.

Q: 129, given 18) Find y'= A) 2y/(2x - sin y) C) - 2x/(2y - cos y) in terms of x and y for an Implicit…

A: Given; y^2+x^2=siny+4

Q: Evaluate each integral. 1. dr VI² - 1 2. I Cos az dz 7x +1 dr 1² – x – 2 3. -エー|

A:

Q: Find div F and curl F if F(x, y, z) = 14y°z°i – 10x°z°j – 5xy°k. 35: 6.8 - div F= curl F=

A: We have to find div F and curl F.

Q: Question 3 of 4 (x² + 1)5 y = (23 – 1) – 1)

A: According to guidelines, we must answer only one question of the multiple questions given. Please…

Q: (2sinx-sin2x' 1. lim x-sinx

A:

Q: INSTRUCTION/S: Evaluate each limit by two methods. TOPIC: INDETERMINATE FORMS FIRST METHOD (Partial…

A:

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 5x2…

A: To write down that it satisfies the mean value theorem or not.

Q: Find curl (2z i + 3x j + 5y k). url(2z i + 3x j + 5y k) = ( i )i + ( )j + ( 3 )k

A:

Q: dy For each of the following functions determine dr

A:

Q: Describe the domain and range of the function. f(x, y) = 3x2 – y Domain: O (x, y): x = 0, y = o…

A:

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

A:

Q: Describe the graph of the equation. r = (7 – 21) i+ 101j O Itis a line in 2-space through the point…

A: Equation

Q: 3 Let F(t) = < 3 2t 3t -1' 3 - 5' 4 -3 Find F (t) F'(t) - < Question Help: D Video Add Work

A: Given: Now, we need to find r→'(t). r→'(t)=33t-1' , 2t3t2-5', 2t24t3-3'        =-93t-12,…

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t++o \ 5t2 + 6' 5t (0,0)

A: Simplify the component wise

Q: Solve the general solution of Differential equation y''-5y'+4y=3e^{6x}

A: differential equation

Q: Consider xy2+x2y=6, find the slope of the tangent line at the point (1, 2)

A: Given query is to find slope of the tangent at given point.

Q: Find r'(t), r"(t), r(t)•r"(t), and r'(t) × r'"(t). r(t)-흑러 - 26 + (a) r'(t) (b) r"(t) (c) r'(t) ·…

A: