Q1. If g = xy - yz - · — zx and F = x²y ī − 2 y²zī – z²x k, find F. grad g and cross product of F and grad g at the point(1, —1, 2).

Q: II. L' Hôpital's Rule. Evaluate the following limits using L' Hôpital's Rule. 3-x 1. lim 1-3 2-8

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the center, vertices, and foci of the ellipse 4x² + y²-8x+4y-8=0.

A:

Q: solve the differential equation dy/dx=2x^4sqrt of y, y.0

A: Solution of given question is written in below steps.

Q: Find the length of the dashed zig-zag path in the following figure. 34 0.75- 0.5+ 0.25+ 00.25 0.5…

A:

Q: y=x² + 8x - 9 -intercept: (x, y) = -intercepts: (x, y) = (x, y) = (smaller x-value) (larger x-value)

A: Given query is to find x and y intercepts.

Q: If a company spends r million dollars on research, it sales will be s million dollars, where r and s…

A:

Q: 11. Determine the divergence or convergence of the following improper integrals and evaluate if it…

A:

Q: Calculate the following two indefinite integrals. Thank you. (6e^(2x)-5x^(3)+(4/x)+3)dx

A:

Q: Find the gradient of the function z(x, y) at the given point P: z = cos(x² + y²), P(3, — 4).

A: The given function is z=cos(x2+y2), P(3,-4).

Q: e2+8i = a + ib, where: a = b i = i

A:

Q: Write the equation for the plane. The plane through the point P(-2,-5,3) and normal to n = (2,7,8 O…

A:

Q: Consider the region B under the graph of y = 3x² + 1, x = [1,3], and above the x-axis. Find the area…

A:

Q: Sketch the lines through the point with the indicated slopes. Make the sketches on the same set of…

A:

Q: Determine how many bags of popcorn should be produced per hour by each worker. Show how this is…

A:

Q: Determine the following indefinite integral. dx X√ 625 + x 2 dx S- x√√625+x² (Type an exact answer.)…

A: We have to determine the indefinite integral ∫dxx625+x2.

Q: Calculate the future value of end-of-month payments of $6,000 made at 2.64% compounded quarterly for…

A: To find the amount after 5 years.

Q: 5. If f(x) = x², g(x) = and h(x) = √x² + 2x, determine the derivative of each composite function. a.…

A: Given: f(x)=x2,g(x)=1x′ and h(x)=x2+2x First find the composite functions and then differentiate

Q: Determine the Laplace Transform of the following functions: a. f(t) = 3te-5t cos(2t) b. g(t) = f(27)…

A:

Q: Consider the function: f (x) = −6x/ 6x^2 − 54 Step 1. Determine the intervals on which the function…

A:

Q: Determine whether the following equality is true or false. √32-x² ₁ f(x, y)dA = √ √₁xY where D =…

A:

Q: it is the empirical formula for C10H20O5 O C₂H5O

A: Empirical formula  An empirical formula is the simplest whole number ratio of elements in a…

Q: y² = 8x,x=2, AOR = Y AXIS

A:

Q: Let f(x) be defined by f(x) = Answer: 3x² + 5x + 2 x + 2 Find f'(1). Note: Your answer (if it's not…

A: Topic - derivative of a function

Q: The slope of the tangent line to the curve y = 4 X at the point 5, is: The equation of this tangent…

A:

Q: Suppose an object is moving along a verticals line. It’s vertical position is L(t)= -t^2 -4t+12.…

A:

Q: Given f(x) = √√x and g(x) = x² - 9, evaluate each expression. (a) f(g(3)) (b) g(f(3)) (c) g(f(0))…

A:

Q: Determine whether the series 2-√√n +∞o Σ √√n n=1 converges or diverges using the Integral Test.

A:

Q: g(x)=3*-1 range y=()*__y=()*__ _y=(3) y =()* YA 2 (y=10²¹ C X O y=5t State the domain and range.…

A: Given  function:- g(x) =3x-1  To find:- Graph, Domain, Range and asymptote

Q: Convert the point (ρ,θ,ϕ)=(6,11π/6,π/2) to Cartesian coordinates. Give answers either as…

A:

Q: 3 The integral ³³ g(x, y) dxdy is equivalent 3 to ₁ ³x g(x, y) dydx

A:

Q: sporting goods store sells 64 tennis rackets per month at $90$ each. The owners estimate that for…

A: Given the query is to find the price to maximize the revenue.

Q: The limit is equal to 1312 Select one: O True O False lim n→∞ 3n 2n³ + 1

A:

Q: 7. The work of an epidemiologist is to investigate the root cause of a disease and determine the…

A:

Q: (a) cos(8): = √2 2

A: answer is in next step. please give a like .

Q: Parameterize the plane that contains the three points (-2,-2,-2), (-12, 2, 12), and (0, 35, 30).…

A: To find the parametric equation of a plane containing three points (-2,-2,-2,), (-12,2,12) &…

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

A:

Q: Q5 a) 100 5² +2³+ [In(Inr)] lim 1+ 7 +6² + [In (In x)] 200 cos x ln(x - *) *-+*+ In (e² - e*) b) lim

A:

Q: Find a particular solution to the differential equation Ур || y" + 5y' + 6y=-108t³.

A: Given differential equation is y''+5y'+6y=-108t3 We have to find a particular solution for it.

Q: 1. Using proper mathematical terminology and different reasoning, explain why there are no solutions…

A:

Q: 8 9 10 11 e centroid of the region displayed in the graph.

A: Topic:- Geometry

Q: Q3. Change the order of integration and evaluate * * dy dx.

A: To evaluate ∫04∫0xdy dx using the change of the order integration. From the limit of integration the…

Q: Find the one-sided limit (if it exists). lim 11x² tan ex Step 1 The sign of the value of x² is…

A: To find the one‐sided limit if it exists.limx→12+ 11x2 tan πx

Q: The cost function for a particular product is given by C(x)=0.001x^3 −0.24x^2 +27.9x +110 dollars,…

A:

Q: Find the volume of the solid when the region enclosed by the curves y=x², x=1, x=2, y=0 is revolved…

A:

Q: `Sketch and find the exact area of the 1) (2 region B bounded by -x y=xe +7, y=x + 9, x =7, and x =

A: As per Bartley guidelines we only give first question answer. Please repost for other parts.

Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

A: We want to find the area of region bounded between the given curves

Q: Find an equation of the line that passes through the point and has the indicated slope. Point Slope…

A: Given that , Point =-3,5 Slope m=-34 Find the equation of the line.

Q: Let f(x) be defined by Find f'(1). f(x) = (2x - 1).

A:

Q: Kiara's grandmother is depositing $1,200 at the end of each quarter into a RESP to s for Kiara's…

A: - Periodic Quaterly Deposit at the end of each quarter is $1200 a). Calculating the Accumulated…

Q: The hypotenuse of right triangle is 74 meters long. The difference between the other two sides is 46…

A: We know that for a right triangle , Let hypotenuse is c and other two sides are a and b. Then…