||r(t) x r"(t)|| Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i + 8 sin(8t)j + 5tk к(€)

Q: Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs…

A: Here we will find all the quantities one by one,

Q: Let floo) = 0e 5 and gloo) = 2a19 Detemine Cgof) (x) 2079. %3D %3D

A: Topic:- function

Q: Find the derivative. ( cos ft dt x10 COS^/

A:

Q: Consider the following vector field. F(x, y, z) = xy²z²1 + x²yz²j + x?y²zk (a) Find the curl of the…

A: div F = i∂∂x+j∂∂y+k∂∂zF(x,y,z) curl F = ∇×F

Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

A:

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(4, 5, 4),…

A:

Q: Show that lim (2,v)>(0,0) **+y D0.

A:

Q: Use the formula for the sum of a geometric series to find the sum or state that the series diverges.…

A:

Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: Match the vector field with its graph. F(x, y) = yi 6. -6+ y 十H HH

A: We need to match vector field with its graph.

Q: A stone is thrown vertically upwards, from the edge of a 5 m tall cliff with an initial velocity of…

A:

Q: Consider the following. f(x) = x(x² – 11x + 35) x2 g(x) %D (a) Use a graphing utility to graph the…

A:

Q: 11. Use the guideline in §4.4 to sketch the curve: f(x) = x² ln x. A). Domain, Symmetry, Asymptotes,…

A:

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A: Given that the number of bacteria in a certain population increases according to a continuous…

Q: ||r(t) x r"(t)|| Use the formula k(t) = to find k(t). ||r"(t)||° r(t) = t'i+ t°j K(t) =L

A:

Q: Find the area of the region enclosed between the curves defined by the equations y = Vx +2 ,y = x ,…

A: Solve the following

Q: S sin x In(cos x) dx X

A:

Q: ind for by Implicit differchtioution 2(xu)

A:

Q: Ben is a fisherman with a boat in Rhyl harbour. This is part of a graph of the depth of water at the…

A:

Q: Let y = 5x?. Find the change in y, Ay when x = 2 and Ar 0.4 Find the differential dy when a = 2 and…

A:

Q: 3. Suppose that the revenue in selling a tables is equal to 200.x -0.25a2 dollars, and producing a…

A: We know that profit=selling price-cost price

Q: Find a particular solution to the DE: y"+ 3y' – 4y = e* xe B. Yp = C. Yp = x²e* D. y, = xe-x E. None…

A:

Q: For the following function, a) give the coordinates of any critical points and dassify each point as…

A:

Q: Use left-to-right elimination to solve the system of equations. 3x + 4y - 5z = 8 4x + y- z = -1 x-3y…

A:

Q: Evaluate using Integration by Parts. (Use symbolic notation and fractions where needed.) хебх+4…

A:

Q: if an open box is to be made using a square sheet of tin, 20 inches by 20 inches, by cutting a…

A:

Q: A concert promoter needs to make $81,000 from the sale of 1800 tickets. The promoter charges $40 for…

A: x+y=1800x= number of $40 ticketsy= number of $70 tickets

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (4, -3)

A: To solve the given line integral.

Q: Let S1 be the hemisphere with Cartesian equation z = 6 – /36 – x² – y? and S2 be the upper nappe of…

A:

Q: the 1. For f(x) = r8/3 - 4x5/3, find a). the domain and f', b). f" (simplify f"), %3D c). the…

A:

Q: Find curl(2: i + 3x j + 6y k). curl(2: i + 3x j + 6y k) = ( )i + ( j + ( )k

A:

Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

A:

Q: Use the log rule of differentiation and differentiate y with respect to x.  y = ln( 8 + ex 8 − ex

A: given function

Q: How would you evaluate |F-dr, where C is the curve with param etrizati on r(t) for astsb?

A:

Q: Consider the double integral XY dA Vx2 + y² I where R is the region of the XY plane, given in the…

A:

Q: D If the Taylor series expansion for f (x) is given by f(x) = Eo- (x- 2)*, then f(4) (2) = %3D

A:

Q: 2. Show that if x and y are two vectors, then

A: Replace x→ by u→ & y→ by v→     Graphing software do not accept label x, y To show: u - v ≤u±v≤u…

Q: The graph of f(x) is shown (see figure). f(x) %3D Vx2 +7 Net draw o scale (a) Find the following…

A: Solution: f(x)=9xx2+7

Q: Question 3 z+3 dx Use the substitution u = 1 - 2. 1 O sec I|+3 sin x+C OIn(1 – a) + 3 sin-1 a + C…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y = 2x, x = 1, and y = 0,…

A:

Q: A region Rxy, in the XY plane, is shown below: A) 1- JJRa 2r + 3y – 6 = 0 2r +3y+1 0 Rry %3D…

A:

Q: Determine the range of f(x,y)=tan 2+x +y

A: Here the value of x2+x2+y3 can vary from -∞ to ∞. The possible values of tan-1x2+x2+y3 is…

Q: Test the convergence of cach of the following two scrics. n" 2n +3 (1) 2 n! (ii) Зп + 2 n=1 n=1

A:

Q: Find the extrema for F&)= Sin Cx) + cos (x) on the interval [o,E| %3D

A:

Q: Evaluate the line integral | -ydx + xdy along the curve C:y? 30x from (30, 30) to (0,0). NOTE: Enter…

A: We need to find integral.

Q: Consider the following planes. -6x + y + z = 6 18x - 3y + 6z = 36 (a) Find the angle between the two…

A:

Q: Consider the function f(x) = 2x° – 15x? – 36x + 8 on the interval [– 5, 9]. Find the average or mean…

A:

Q: Find div F and curl F if F(x,y, z) = x°i – 5j + yzk. - div F= curl F=

A: A detailed solution is given below

Q: An Easter ham is put in the oven with a temperature probe embedded in the center. Assume the…

A: We are given that, an Easter ham whose temperature is 40° is kept in an ovan whose temperature is…

Q: ) Find p(3). ) Find p(13). =) Find p(13)-p(3). p(13)-p(3) 1) Find and interpret this result. 13-3 -)…

A: Given query is to find the value of the function at indicated points.