Next we substitute 'x s(x) = √² f* VI √ 1 + (f'(t))² dt 4 = dy dx - [~ √₂ + ( ₁6(+) = 1 3x J = 3x¹/2 1 + into the equation for the arc length function and simplify. X t dt 2 +²/2) ² dt

Q: Given the demand equation p + =40, where p represents the price in dollars and x the number of…

A:

Q: Write an iterated integral for dA over the region R bounded by R y=ex, y = 1, and x = In 3 using a.…

A: Here we have given an iterated integral over the region  bounded by:, and .

Q: 3) Maclaurin expansion

A: f(x)=3xsinhx+cos√6-1

Q: On a 600 mile road trip, two people drive the car. One person drives three times as long as the…

A: Given  :

Q: Make a vector field plot of the differential equation. Find any equilibria of the differential…

A:

Q: Integrate the item using its desired method; - Trigonometric & Algebraic Substitution Partial…

A: Factor the denominator:  Perform partial fraction decomposition:  Apply linearity:

Q: 2) Use the given graph of f(x) to estimate the area under the graph, over [0,3] using 6 rectangles…

A: We have to Determine area under the graph.

Q: If tant = 9 2' what is tan (t - π)? Enter the exact answer. tan (T) A Pa € 90 b Show your work and…

A: To solve the following trigonometric problem

Q: Eng. Translating: Expand the function to the f (x,y) = ecosy at (0,0). Taylor series

A:

Q: Sketch the region of integration and write an equivalent double integral with the order of integra…

A:

Q: Differentiate y = Σ (k + 4)ak+8. k=0 y=Σ k=0

A:

Q: Solve the following set of equations by graphing. y+ x = 9 3y= 2x+8 Stan O (3.75, 5.25) O (3.8, 5.2)…

A: we have given Two equation  y+x=9       equation (1)and   3y-2x= 8      equation (2)

Q: Find the parametric equations for the line through (2, 4, 5) perpendicular to the plane 3x + 7y - 5z…

A:

Q: Given the demand equation x = 10 +20, where p represents the price in dollars and x the number of…

A:

Q: (x(t) Find a plane containing the point (-5,-7,-4) and the line y(t) z(t) = = -8 + 8t 7 - 6t -5+7t

A:

Q: Find Vf at the given point. -1 f(x, y, z) = ex+y sin z + (y + 4) cos x, (0,0,1) f(0,0,5) = (³-4)i +…

A:

Q: Suppose f(x) = 3x² + C, where C is any real number. Then the expression can be written in the form…

A:

Q: Compute the length of the curve r(t) = (4t² + 8, 61²-5, 1³) over the interval 0 ≤ t ≤ 2.

A:

Q: Find the equation of the parabola with the given properties Vertex (0,0), focus (8,0). = x

A:

Q: Use a geometric formula to find the area between the graphs of y=f(x) and y = g(x) over the…

A: Here we have to find the area between the two curves

Q: The following f(x) = 3 cos +9 function represents the depth of water at the end of a boat dock where…

A:

Q: The figure shows a lamina that is shaded according to the given density function: darker shading…

A: Given:Estimate the location of the center of mass of the lamina.

Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

A: The given function .We have to show that has a removable discontinuous at and find the value of…

Q: Find  gx  and gy

A:

Q: S

A:

Q: Treath as a constant. For what values of h (if any) does the following equation have equilibria? Use…

A:

Q: Use polar coordinates to find the volume of the given solid. Under the paraboloid z = x² + y² and…

A: Given that  a paraboloid and a disk if we let   then we have Now we  have to find out the Volume of…

Q: Consider these 2 functions f(x) = fex ifxco 1+/6x² if x>0 g(x) = e¯* In (f(x) −2) What is the domain…

A: The functions are

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) =…

A:

Q: Find the absolute maximum and absolute minimum of the function z = f(x, y) = xy + 4x - 2y + 4 on the…

A:

Q: Let f and g be the functions in the table below. g(x) 2 3 1 X 1 2 3 f(x) 3 1 2 (a) If F(x) =…

A:

Q: For the slope field shown, which could be a family of anti-derivatives? TU 1 +-111 5-111

A: We are asked to find which of the following equation would matches the field

Q: Consider the following differential equation (tan y − 2)dx + (x sec²y + dy = 0, y> 0

A:

Q: 2 Evaluate the definite integrals using the graph of f(x) below. (a) ² y 4 2 6 (c) √° f (x). 0 -2-…

A:

Q: What is the function.  Is it 30 - (1/1000)x

A: We have to determine the function.

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

A:

Q: When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the…

A:

Q: Consider the line integral: I= [(12x-y) dx+(7x+5y) dy where Cis the circle x² + y² = 1 in the…

A:

Q: There are two times the amount of milk chocolate bars as there are dark chocolate bars in a box. If…

A:

Q: Find an equivalent double integral with the order of integration reversed. (6-3) 2 S. S dyda So y =…

A:

Q: Find all intervals on which the function is positive and all intervals on which the function is…

A:

Q: Compute the arc length function s(t) = f ||r' (u)|| du for r(t) = (6√/2+¹/2, In(t), 9t) a = 1 (Use…

A:

Q: Integrate f(x,y) = x² + y² over the triangular region with vertices (0,0), (1,0), and (0,1). The…

A: Given:f(x,y)=x2+y2 over the triangular region with vertices (0,0), (1,0),(0,1)

Q: Find the equilibria of the differential equation =4+5x+x? Identify all the equilibria. dx dt X =…

A:

Q: Write an iterated integral for da over the region R bounded by R y = 5√√x, y = 0, and x = 32 using…

A: we can see from the figureThe bounded grey region represents the region R.

Q: U(x,y)=(x+2)^2(y+3)^3 Find the partial derivative of x and y

A: U(x,y)= (x+2)2(y+3)3We have to find partial derivative of x and y

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x +12y + 18% on the elipse…

A: Given function

Q: Find the lengths of the sides of the triangle PQR. P(1, 2, 4), Q(3, 4, 3), R(3, -2, 0) |PQ| = |QR| =…

A:

Q: A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find…

A:

Q: where T is measured in degrees and x, y, z in meters. a) Find the rate of change of temperature at…

A: