An 6 in x 10 in sheet of paper is to be folded into a box, with one side open, by cutting squares in the corners and folding up the flaps. How big should each square be (in inches) if the volume of the box is to be maximized?

Q: Q1- Find all the second-order partial derivatives of the function: s(x, y) = tan-¹(x)

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Q: f(x csc² 4x - x cos 4x)dx

A: The answer is given below:

Q: Hả+b+c = 0, show that ả x b = b xả = xã

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Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

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Q: f is continuous on (a, b) then there is a number c in (a, b) such that f(c) is an abso inimum value…

A: Topic:- calculus    Definition :-  Extreme Value Theorem   If a function f(x) is continuous on a…

Q: Find an equation for the line tangent to the graph of y = tan ¹ (2x) 2 1 What is the tangent line to…

A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative…

Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: Consider the function f(t) = = -X 3-x (x − 3)² - if x 3

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Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized?

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Q: 4dx 3r x-√√x² S

A: Let's solve given integral.

Q: A Л The path r(t) = (4 sin t) i + (4 cos t) ] describes motion on the circle x² + y2 = 16. Find the…

A: The path r(t)=4 sin ti+4 cos tj

Q: Evaluate the integral: 18x² √64 x² - I dx

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Q: Find the Volume: Rotate the region bounded by x = y²-6y + 10 and x = 5 about the y-axis

A: A detailed solution is given below.

Q: Let u = (a11, a12, a13), v = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R³. Explain,…

A: let  x, y, z  be the non zero  vector that is orthogonal to   u, v and w

Q: 15. f (sec² x) dx / (√(1-4 tan² x))

A: Hi and thanks for your question! Unfortunately, as per our guideline, only one question should be…

Q: Find the constants a and b such that the function is differentiable everywhere. x²-9 x+3 if x < -3…

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Q: Find a cubic function y=ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local…

A: According to our guideline the answer to answer only the first question if you want any particular…

Q: Please write the complete solutions. Upvote will be given! Consider the region bounded by y = x3, y…

A: Please write the complete solutions. Upvote will be given!   Consider the region bounded by y = x3,…

Q: Find the Maclaurin series for f(x) = ln(1+r) using the definition of a Maclaurin series. Also, find…

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Q: 15. A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No…

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Q: 12. Setan 2x sec² 2x dx

A: As per guidelines we can solve only one questions at a time, so if you need more answers kindly…

Q: The distance between the points (-8, m) and (m, 9) is 13. What are the possible values of m? a) 3 or…

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Q: Determine using Cauchy Riemann equations the function below is analytic or not? f(2)=x² + y² - 2xy

A: This question can be solved using the concept of the two conditions of Cauchy Reimann for a function…

Q: a. b. Evaluate the following integrals 2 dx cos²x√4 tan x- tan² x I [ sin(√a)da dx

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Q: ff is continuous and ƒ(5) = 2 and ƒ(4) = 3 then lim ƒ(4x² — 11) = 2. x→2 True False

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Q: dy For the following composite function, find an inner function u = g(x) and an outer function y = f…

A: We need to find derivative.

Q: 4dx x- 3√x²

A: Evaluate the integral

Q: Complete the parametric equations for the line where the planes - 7x + y + 3z = 3 and 4x7y + z = 23…

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Q: dy For the following composite function, find an inner function u = g(x) and an outer function y = f…

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Q: f(x csc² 6x - x cos 6x)dx

A: Given, ∫(x csc2 6x-x cos 6x)dx

Q: of the given conditions. lim f(x) = ∞, Sketch the graph of an example of a function f that satisfies…

A: Topic:- limits

Q: 26. b) Given four points A(-2, 0, -3), B (1, -2, 1), C (-2,-3,2), D ,0). Find the equation of the…

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Q: Given z=x²y+3xy4, x=sin(2t), y=cos(t), find dz/dt when t=0

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Q: xdx ax + b cos ln x dx X S 2, A = 0

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 Iny [the Low +¹Y2 ex+y dxdy 0

A: See the details solution in below

Q: g(x) = (1 Use the power series expansion of f(x): = 1 x)² 1 for x< 1 to find a power series…

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Q: I need a solution here. Help please c. Five people ,of whom three are women and two are men, are…

A: Given

Q: Cn = COS * ´π(1+4n)` 2

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Q: KIN T 2 2 6² 6³ 6² 0 0 ¢sinr do dr de

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Q: 20. Stan² x dx

A: Consider the integral  ∫tan2x dx

Q: Use the transformations to graph the given function. Show all translations on each transformation.…

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Q: ππ 2 CAP• 0 0 0 ¢ sinr do dr dộ

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Q: Find an equation of the line tangent to the curve tan¹(y) = (x+y)e at the point (0,0). tan ¹(xy) =…

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Q: What is the mass of body if the exerted force of 10 N is accelerated by 5 m/sec^2? O 4.5 kg 1.5 kg O…

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Q: Water is poured at a rate of 10 cubic meters per minute into a conical tank 6 meters across the top…

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Q: (x²+2) dx x+2

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Q: Find the vector product (a*b) of the * two given vectors a= 2i+3j+4k, b=3i+5j, here i,j&k are unit…

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Q: Get a similar question = y = 5√x. and the change in y, Ay when x = 2 and Ax = 0.2 nd the…

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Q: Evaluate using Partial Fraction Decomposition: (- dx

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Q: Q4- Solve the following differential equation: (1 + x²) dy + (y - tan-¹(x)) dx

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