Find the gradient of the function at the given poin w = x tan(y + z), (6, 15, –13) Vw(6, 15, –13) =

Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

A:

Q: Find a possible formula for the graph. -8 -7 -6 -5 4 -3-2-1 5678 O g(x) = kx(x + 1)(x– 2) for any…

A:

Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 2. у — С1 3D С2е -4х 2. у —…

A:

Q: An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal…

A:

Q: (b) If a > b and c > 0, then ac > bc.

A:

Q: der the following planes. 5x + 2y – z = 44 x – 4y + 2z = 0 (a) Find the angle between the two…

A: Angle between planes and line of intersection of planes

Q: Find f if f(x) = tanh (sin e*). -1 %3D e* Cos e* Cos e* 1- sin? e* | O Option 1 Option 2 e cos e* 1.…

A:

Q: (w°t wz? -z) dw +(z² tw² -w) dz= 0

A: Let's find.

Q: What are the relative extrema of the function f(x)=x3+3x3-24x+7

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: This question is based on 3d line equation.

Q: Consider the function y = 5x4-4x3-3x2+8x-12. What is the average value of the function on [-3, 1] ?

A:

Q: dx Assume that x= x(t) and y= y(t). Let y =x +4 and -5 when x= 1. dt dy Find when x= 1. dt

A:

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A:

Q: Evaluate the following indefinit 4. Ssin'x cos*x dx

A:

Q: Materm tvamare the inte aral:\

A: This question is based on indefinite integral.

Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: We have to find value of given definite integral.

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A: Given: Here, M=2x-2y2, N=12y2-4xy. Notice that ∂N∂x=-4y=∂M∂y. So, the function is exact.

Q: - Find the Taylor series expansion for the given function about x =g. :- Using the Taylor series…

A:

Q: In trigonometric substitution where the integral involves va? + u², what must be the value of the…

A:

Q: 1) y= 3cos 4 +2 4 a: b: Period: d: Phase Shift: S C:

A:

Q: Learning Task 1: Directions: Solve for y in terms of x (isolate y on one side of the equation and…

A:

Q: d. x cosy + y sin x –1 = 0 3 х е. = 2 x y

A:

Q: Let a = (– 9, – 4, 1) and 6 = (10, 4, 5). Compute the projection of a onto b and the vector…

A:

Q: Where is the function decreasing? * (-1,3) (-2,1) (0,1) O (*-1) O (*, *) O (-1, ) O (-*, 3)

A: A function is said to be decreasing in an interval in which on increasing the value of x, the value…

Q: In xdx

A: Formula:Integration by parts:∫ uv dx =u∫v dx -∫ dudx∫vdxdxI=∫ x5 ln x dxu=ln x, dudx=1xv=x5I=ln x ∫…

Q: e* +e* –x? - 2 Lim sin? x– x? 2

A: To solve the given limit of the function

Q: Consider the function  f(x)=4/x^2−3/x^5. Let F(x) be the antiderivative of f(x) with F(1)=0. Then…

A:

Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: 4.

Q: What is the lateral area of a cylinder with a height of 7 cmand diameter of 240 mm? 3360π cm2 1680п…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of v. g(a,…

A: Let's find.

Q: Use vectors to show whether or not the points form the vertices of a parallelogram. (1, 1, 3), (4,…

A:

Q: VECTOR DIFFERENTIATION: If R = e^(−t) i + ln(t^2+ 1) j - tant k. Find: (a) dR/dt, (b)…

A: R=e-ti+ln(t2+1) j-tant k

Q: Solve the following items and show your solutions. a.) Find the general and particular solution of…

A: x dydx+2 y =4x2dydx+2x y =4xComparing with Bernouli's equation;y'+P(x) y = Q(x)P(x)=2x, Q(x)=4x

Q: (x² + y² ) dx – xydy = 0 O 2y = x In cx² O y? = x² In cx²

A:

Q: Solve for the following application of first order differential equations. Show your solutions. 3. A…

A:

Q: A function f(x) passes through the points (15,24), (18,37), and (22,25). Use the Lagrange Formula to…

A:

Q: (3 - 2 3 – 4cos dx

A: The given integration,     ∫3-4cosxπ2 dx

Q: A number is one more than thrice the other number. What is the minimum product of the two numbers?…

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A:

Q: True/False: The saddle point of the of the function f(x,y) = x² – e occurs at (0,0). - O True O…

A:

Q: Solve the following initial value problem. dy 1 --X, x> 0; y(6) = 3 dx x2

A:

Q: 2. The growth rate (in inches per year) of the diameter at breast height of a certain tree is given…

A:

Q: Let S be the solid obtained by rotating the region shown in the figure about the y-axis. a = 4 b = 2…

A:

Q: 2. Find the differential equation of the family of circles having their center on the y-axis.

A:

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A:

Q: Let à =, B = and Č = a) (à · B)č b) Ả · (2C) Find C)

A: A→=1,-2,3, B→=0,2,4, C→=5,-1,-3a)…

Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

A:

Q: 1 EVA LUATE ECs) OF THE DIFF ARD 4(0)-0. dy dt² dt

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: dy J 1+y+1

A: