3. From a thin piece of cardboard 14 in by 14 in, square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is that maximum volume?

Q: 3. Apply the Integral Test to show whether or not the series converges. You do not have to show the…

A: We have to find the convergence test

Q: 1²e¹dV where E is bounded by the parabolic cy E

A: the answer is give in step2

Q: H J A: x = B: x= C: x = D: x= E: x= F: x= G: x= H: x= Identify the points of the circle above. 1: x=…

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

Q: x, evaluate each expression.

A:

Q: (a) Find the derivative of ƒ (2) = (x² + 5) (8æ — 5) by first expanding the polynomials. Enter the…

A: We have to find out derivative

Q: Find the TOTAL SOLUTION of the following Differential Equations: 1. 3 dy. dy +3 dt³ 2 dt² - 4 = 5t²…

A: Given the differential equation is d3ydt3 + 3d2ydt2 - 4 = 5t2 + 4

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

A:

Q: When Newton's Method is used to approximate the root of f(x) = x³ + 2x² - 1 in in the interval [0,…

A:

Q: Consider the following differential equation to be solved by variation of parameters. y" + y =…

A:

Q: Compute the gradient vector fields of the following functions: A. f(x, y) = 1x² +10y² Vf(x, y) =i+ j…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A:

Q: on the closed triangular region with vertices (0, 0), (9, 0) and (9, 11). List the minimum/maximum…

A:

Q: Write an expression for the polynomial of least possible degree graphed below. Leave your answ…

A: The solution is given below

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

A:

Q: Problem 2.3 Evaluate 2x² + 3x + 1 2x - 3 lim x-1 x².

A:

Q: 16. x²y" (x) + 5xy' (x) + 4y(x) = 0 ; y (1) = 3, y' (1) = 7 17. x³y"(x) + 6x²y"(x) +29xy' (x) -…

A: The given differential equation is;  x2y''(x) +5xy'(x) +4y(x)=0, y(1)=3, y'(1)=7.

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

A:

Q: teeeee Find the vector v with the given magnitude and the same direction as u. V Magnitude ||v|| =…

A:

Q: Given that the graph of f(x) passes through the point (4, 2) and that the slope of its tangent line…

A: Recall: The slope of the tangent line to the curve f(x) is f'(x).

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

A:

Q: sina+sinatan² dx a sinx 2. ·S

A:

Q: Solve the equation for exact solutions in the interval [0°,360°). Use an algebraic method. 2 4 sec 0…

A:

Q: Evaluate the triple integral of f(x, y, z) = cos(x² + y²) over the solid cylinder with height 8 and…

A:

Q: Use implicit differentiation in finding y' . x²y+xy² =6

A:

Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

A: To find the component form of v given its magnitude and the angle it makes with the positive…

Q: 4. A tank with a volume of 1800 gallons originally contains 1200 gallons of fresh water. The first…

A: Follow the procedure given below.

Q: 1. Function f is continuous on (-00,00). Find constant k. f(x) [kx² + 2x x-kx if x ≥ 2 if x < 2

A:

Q: n zise me gebrac ve do chang Find the extreme values of the function and where they occur. y = x³ -…

A:

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = P(2, 3, 4),…

A:

Q: e 1 Determine the equation of the tangent line y=x=2( at x

A:

Q: 'y-1 ++ Beson Muss 1- +

A:

Q: NOTE: Enter the exact answers in terms of i, j and k. (a) Same direction as 2i + 5j. -2 √29 u v (b)…

A:

Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

A:

Q: Find the derivative of the function using Chain Rule. (2x-6)-¹ (x²+3) h(x)=

A:

Q: 4 3 1 -1 & Find lim The graph of the function f(x) = tanx is given above for the interval z = [0,…

A: Topic = Functions

Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A: To find the critical points of the following function. By using the Second Derivative Test to…

Q: (a) to x = 8. Find the area of the region enclosed by y = x² - 4x and y = 2x from x = -2

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Given f(x) below, find f'(x). f(x) = z" t' dt √z

A: See this solution in below

Q: Point Line (-7, 1) x+y=8 Exercise (a) Write an equation of the line through the point parallel to…

A: This question can be solved using the concept of point slope form of a line.

Q: 3. [x²cos2x dx

A: The given integral, ∫x2cos2x dx Note:    Multiple questions are given, we are answer only one…

Q: State the restriction on the domain and then find the inverse of the function. f(x) = x² - 6x Domain…

A: The given function is fx=x2-6x

Q: Evaluate the function for the given value of x. r(x)=3x, p(x)=x2+6x,(p-r)(x)

A:

Q: If you invest $5000 compounded continuously at 4% p.a. how much will this investment be worth in 5…

A: The initial amount P=$5000 Rate of interest r=4%=4100=0.04 p.a. The time period t = 5 years

Q: Average Cost Graph The total daily cost (in dollars) of producing a mountain bikes is given by…

A:

Q: Consider the following planes. -6x + y + z = 6 24x - 4y + 6z = 36 (a) Find the angle between the two…

A: Given problem:- Consider the following planes. - 6x + y + z = 6 24x - 4y + 6z = 36   (a) Find the…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

A: here is the solution:

Q: What is the original price of P1,743,759 discounted price at 22% discount?  (whole number)

A: discounted price = 1,743,759  discount rate = 22%  find original price = ?  this discounted price is…

Q: 3 y = (²x2 ²³-6)9 Find day doc2

A: Solve the given differentiation

Q: 3 12 Find the exact value of sin (a + B), if sin a= and sin ß= 5 13' sin (a+B) = ? OA. -16 65 OE. 33…

A: Given that sin α=35 and sin β=1213, with α and β in quadrant I

Q: 2. Find lim (√x + 2 = √2).

A: