Determine whether F(x, y) = 2x²y i+ 8xy' j is a conservative vector field. If so, find a potential function for it. F Choose one Choose one is a conservative vector field is not a conservative vector field

Q: Determine an equation of the line tangent to the curve Y = 5x-4 at the point with x- coordinate 4.

A:

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

A:

Q: Using any method, find the value of F. dr if F(1, у) — (бе" + ye")i + (e* + 5xe") j and at C :r(t) =…

A:

Q: 구. ( 34 Cxtd) ax An 14 X? (X-1)

A:

Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: T X =…

A:

Q: Q8. Identify the function, whose derivative is defined below: (x + h)2 – x? dy - lim dx h→0 h A.…

A:

Q: dy 1. Find for the following: dr :b. y sin y = ry

A:

Q: Find an equation of the tangent line to the given curve at specified point. (1, 1/4).

A:

Q: Describe the graph of the equation. r = 5 sin 14ti + 5 cos 14t j O It is a circle of radius 14 in…

A:

Q: Clairaut's Theorem Let DCR be a disk containing the origin and assume that q : D → R is a function…

A:

Q: Use local linear approximation to estimate (31.62)4.

A:

Q: Evaluate the definite integral. (Use symbolic notation and fractions where needed.) dx %3D VI- - x2

A:

Q: Find the arc length L of the graph of r(t). r(t) = 12 cos(t)i+ 12 sin(t)j + tk, 0<t< 2n L= 75.66

A: arc length

Q: Calculate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

A:

Q: 1 O Evaluate lim (3" + 7")

A:

Q: Calculate r1(t) · r2(t)] and (ri(t) × r2(t)] first by differentiating dt the product directly and…

A:

Q: The revenue of an online retailer increases by $320,000 every year, this is an example of…

A: We will find if this is exponential.

Q: Integrate the square root of sin (In x) dx * O x/2 [ sin (Inx) + cos (Inx)] + C x/2 [ sin (Inx) -…

A: Given

Q: In the integration What is the implicit derivative of u? V9-4x² a. du = 2dx b. du = * - 2dx c. du =-…

A:

Q: 10. Using the graph below of the function f(x), identify the approximate interval(s) where the first…

A: Given that,

Q: The total cost function is given by the fixed costs minus the variable costs. True False

A:

Q: Evaluate the integral of sec^5 (x) tan^3 (x) dx * 1/7 sec^7 (x) - 1/5 sec^5 (x) + C 1/3 tan*3 (x) +…

A: Given: I=∫sec5xtan3xdx   As we know that; The trigonometric identity; sec2x=tan2x+1 The Power rule;…

Q: Evaluate the integral of the following using Miscellaneous Substitution X Sdx 1+x 5.

A:

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

A: Using greens theorem

Q: Use Green's Theorem to evaluate the line integral. Iy? dx + xy C: boundary of the region lying…

A: A detailed solution is given below

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

A:

Q: Match the vector field with its graph. F(x, y) = xi + 3yi 1信 5.

A:

Q: Verify Green's Theorem by evaluating both integrals v² dx + x² dy = / / dA ax for the given path. C:…

A:

Q: A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The…

A: Here, the given concentration function is: C(x)=0.9x2 where x is the distance away from the plant in…

Q: [6x? arcsin(x)]dx

A:

Q: Let T: R - R be a linear transformation such that T(1, 1, 1) = (4, 0, -1), T(0, -1, 2) = (-5, 4,…

A:

Q: Find the arc length L of the graph of r(t). r(1) = t³ i+ t j+V6r? k, 2 <t< 5 k, 2 <t < 5 L = i

A: Given : r(t) = t3 i + t j + √6 t2/2 k 2 ≤ t ≤ 5 Now, r'(t) = 3t2 i + j + √6 t k Arc Length :

Q: Describe the graph of the equation. r = 8 sin 5t i + 8 cos 5t j O Itis a circle of radius 8 in the…

A:

Q: dy for each of the following: (2 p dx 5. Find (a) y=|(cost+e' – sint+3t³ )dt 3. csin x (b) y = (t2 +…

A:

Q: Q9. Which of these is not the derivative of the function, y = x": A. -½x-1½ B. –0.5x-1Vx-1 C. –0.5 1…

A:

Q: Suppose that a, b, and c are unknown constants such that f(x) = x² + ax + b and g(x) = e(3z–3) %3D…

A:

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 8)

A: Here we have to evaluate        ∫c (2x-y)dx+(x+3y)dy

Q: Let f (x) = x(8+6x). Evaluate the definite integral 1 rOF So f (x) dz. (F(1)]* Enter the value of…

A:

Q: y? = x and y2 = 2 – x %3D

A:

Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

A:

Q: H.W: Use the comparison test to determine the following series converge or diverge: 1 3" +5 n=1

A:

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A:

Q: 4x + 2(x+1) ≥7+x

A: Solution: According to your given question, we are solving for x 4x+2(x+1)≥7+x

Q: Find an equation for the tangent line to the curve parametrized by x = 4t y = est at the point t =…

A:

Q: Which of these statements is False? А. (а?)3 — а6 Вв. а?а — а = a' a2 C. a3 = a-1 D. a? + a³ = a°

A:

Q: 00 1 dx x(Inx)2

A:

Q: Evaluate the indicated partial derivatives. z = 6a?y – 4a°y dz dz ду

A:

Q: Find the limit. lim (t i – 4 j + t k) lim (t i – 4 j+? k) i i+ i j+ i k

A: The given limit is; limt→9t i-4 j +t2 k

Q: Evaluate (2x – y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 5

A: To evaluate line integral over X axis ,take y=0 and dy =0.

Q: Use the function to find the image of v and the preimage of w. T(v,, v v,) = (4v, - v,, 4v, + 5v,),…

A: