Find an equation of the plane containing the point P (1, -7,1) and the line r (t ) = <3 − 2t, 4t, 7> .

Q: Use Green's Theorem to evaluate the line integral along the positively oriented curve C that is the…

A:

Q: Find the solution of the given initial value problem. ty' + 4y = t²t+7, y(1) = 2, t> 0

A:

Q: Question Find the linear approximation L(x) of the function f(x)=√x - 10 at a = 26. (Enter an exact…

A:

Q: Find the vector v whose initial and terminal points are given below. (5.5,2.1), (9.5, 6.1)

A: Recall: The vector v with initial point (x1,y1) and terminal point (x2,y2) is, v=x2-x1, y2-y1 We…

Q: If a rock is dropped from a height of 237 ft, its poistion t seconds after it is dropped until it…

A:

Q: Find an equation of the plane. the plane through the origin and the points (4, -5, 2) and (1, 1, 1)

A:

Q: x dy-y dx = x3 dx y" Answer: 4x + x4y + x¹y = Cy.

A:

Q: The formula for the volume of a cone is given below. Find the rate of change of the volume for each…

A:

Q: Jxy co R xy cos y dA R: -1≤x≤ 1,0 ≤ y ≤

A:

Q: 4 Find the arc length of the curve the interval 2≤+ ≤ 5 3 given parametrically by x= 3 + ² y = + ²,²…

A: To find out the arc length of the curve.

Q: 1. Find the maximum value of f(x, y, z) = x + y − z subject to the constraint x² + y² + z² = 6.

A: f(x,y,z)=x+y-z   x2+y2+z2=6 Rewrite it as: x2+y2+z2-6=0 L(x,y,z,λ)=(x+y−z)+λ(x2+y2+z2−6) Find all…

Q: 12. Find an equation of the line tangent to the curve at the point corresponding to the given value…

A:

Q: Evaluate the line integral along the curve C. S-Tabe − ydx + xdy, C: y² = 3x from (3,3) to (0,0) O O…

A:

Q: Find the derivative. [미 In dx x +3 x-3

A:

Q: Use Divergence Theorem to evaluate SF. Nds and find the outward flux of F(x,y,z) = xi+y²j−zk through…

A:

Q: 4 In the following differential equations, test for exactness and determine the solution of each: 1.…

A:

Q: For which of the following infinite series does the Ratio Test fail? IM8 IM8 k=0 k 5k そそ n=1 (n +…

A:

Q: to find all the second order partial derivatives of the given function. The function is f(x, y) =…

A:

Q: The system x' = cos(t)x+ sin(t)y y' = cos(t)x - sin(t)y is linear.

A:

Q: Determine whether the equation is exact. If it is exact, find the solution. (e'siny + 3y)dx -…

A:

Q: Find the radius of curvature of the curve y = √√x at x = 1 5√5 2 5√5 b) Sys c) 5√5 d) none 2 a) ind…

A:

Q: [ (x − 7) sin(x) dx

A:

Q: Find the average value of the function over the given interval. F(x) = = 2₁ [4, 6]

A: We have to find the average value

Q: Funktionen f(x) har följande graf: -3 -2 w 1 101 5- -10- Vilken, eller vilka av funktionerna nedan,…

A: Disclaimer: since you have asked multiple sub parts of a question, we will solve only first three…

Q: Question Find the change in volume dV if a circular cylinder with radius r (Round your answer to the…

A: Volume of a circular cylinder is V=πr2h

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.03 cm /…

A:

Q: 3. Determine the point(s) where the function y = ₁ , has a maximimum and/or a minimum. Find BOTH…

A: Determine the point(s) where the function below has a maximimum and/or a minimum. Find BOTH…

Q: What is the directional derivative of f(x,y,z) = ln(x²+2y²+ 4z²) at the point P(-1, 2, 4) in the…

A: The given function is; f(x,y,z)=ln(x2+2y2+4z2) Point P(-1,2,4) u=-3i/13 -4j/13 -12k/13.

Q: Find the particular solution of the differential equation that satisfies the initial equation= f(x)…

A: We have differential equation f"(x) = 7/x2  and initial conditions f'(1)=3 and f(1)=4

Q: If R = {(x, y) : 0 ≤ x ≤ 1,0 ≤ y ≤ 1}, then find (²+1) +2 0 1 arctan O 2√2 3 0 √2 3 O √2 3 (√³/₂2)…

A: Please see the below picture for detailed solution.

Q: n-1 3n-1 Determine whether the series Σ=1 is convergent or divergent. If it is convergent, find its…

A: Using Cauchy criteria find that series is divergent

Q: The eigenvalues of a square matrix A are the numbers À for which the matrix A-XI is regular.

A:

Q: please write on the paper. I dont know how to write it. Thank you

A: Given function:- f(t) =(e2t -e-2t)2

Q: B) Use a known series to express ƒ(x) = e¯ as a Taylor series.

A: We need to use a known series to write the given function as a Taylor series.

Q: 2) Determine as derivadas parciais de 1ª ordem das funções z=2e² sen(x) P(1,5). (valor: 1,0) no…

A:

Q: Find the area enclosed by the polar r = 2 (1+sine) Curve

A:

Q: Q4) A- Graph the following functions and determine (domain, range): (1) y=sin/x/ (2) y=/x²-2/ (1) y…

A:

Q: Find the differential equation of the family of circles with centers on the line x – 2y = 3 and…

A: Given:  circles with centers on the line x – 2y = 3and passing through (3, 0).

Q: Screenshot (16 Find the solution of the given initial value problem in explicit form. 1 y' = (1 -…

A:

Q: Let f be a function defined for t 2 0. Then the integral {f(t)} =[e-stf(t) dt is said to be the…

A: We need to find Laplace.

Q: Solve: y" + 4y = x² + ex Yc=C1+C2_ Type the letter corresponding to your answer. Yp=A A_____ B с = A…

A:

Q: Let f(x)= I Determine f'(x). sin² (³+1) dt, x= [1,1].

A: Given: f(x)=∫-xx2sin2(t3+1)dt

Q: 1. Solve x²-3x²10x + 24-0. Show at least one long division process.

A: Let P(x)=x3- 3x2 - 10x+24 P(2)=23- 3(2)2 - 10(2)+24=8-12-20+24=32 When x=2, p(2)=0. Thus x-2 is a…

Q: 5. The graph shown here is the graph of g'(t). area = 2 area = 2 PUA 5 We know that g(0)=5. Use this…

A:

Q: Nx - My If = R, where R is a function depending only on the quantity z = xy, then the differential…

A:

Q: 16 x0.67.dx

A: Formula  ∫xndx=xn+1n+1+c

Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = G(s), then ¹{F(s)G(s)} = f(t)g(t). O True…

A:

Q: polar curves. 63. The complete circle r = a sin 0, where a > 0

A:

Q: Evaluate the following indefinite integral: [sec ³0tan odo

A: The objective of the question is evaluate the indefinite integral.

Q: Find the conservative vector field for the potential function h(x,y,z) = 16xy ln(x+y) by finding its…

A: