A closed box with square base and vertical sides is to be made from 150 square feet of cardboard. What dimensions will provide the greatest volume?

Q: Question af If f(x, y) = xy² - x ln(y) find Ət if x(t, s) = s² - st³ and y(t, s) = e-st²

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Q: Find and classify the critical point of f(x,y) = -³y² - xy + y²³.

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Q: Find the smallest number of terms of the series Σ1 partial sum sn is within of the sum. 1 100…

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Q: A region is bounded by the curve y = √√2 - x and the lines y = -x and the x-axis. The integral…

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Q: If then fyx (1,0) = ? Select one: 0 - sin y -2 None of them 2 f(x, y) = 2x cos y,

A: The required partial derivative is evaluated below.

Q: If f(x, y) = x³y + cos(x) then (fa, fy) = (3xy - sinx, x³). Select one: O True O False

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Q: Find concave upward and concave downward of 6x^2-x^3

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Q: 7. The critical points of the function f(x) = 1³-272 are (a) ±3 (b) ±1 (c) +√2 (d) 1

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

Q: f(x, y) = 75 + 8x+5 Find fx, fxy, and fxyx. 8x³ e-8y

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Q: and x = = z = e-22 In (2-y), Select one: O True O False - 6t, y = t-s, then the value of 3 is equal…

A: In this question we have to find whether the given statement is True of False.z=e-2x…

Q: 3. (y + ²+ ) dx + (x + xy²)dy = 0 3 2

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Q: If f(x, y) = 2√√x² + y2 - 16, then the domain of f is the set D = {(x, y) x² + y² ≤ 16}. Select one:…

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Q: The annual number of passengers going through Hartsfield-Jackson Atlanta International Airport…

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Q: A graph of a model for the sales of services between 2004 and 2008 by a leading global provider of…

A: We have to find the solution of given question.

Q: Integrate: S (2x2-10x+15) gở ba tô 2x + 3 ln() + C ○ 3 ln()+ +C O 2x+3 ln()+ ○ 3 ln() + C +C dx

A: ∫(2x2-10x+15)x2-5x+6dx=∫(2x2-10x+12+3)x2-5x+6dx ∫2(x2-5x+6)(x2-5x+6)dx+∫3(x2-5x+6)dx…

Q: k will the function f(x) = kx²-x²³ have a point of inflection at x=2? For what value of

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Q: The figure has a tangent line drawn at a labeled point. 9500 9400 9300 9200 9100 p(t) thousand…

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Q: The graph below is a transformation of the absolute value function f(x) = |x|. Write the equation of…

A: We have to find the equation of transformed graph.

Q: Use a triple integral to find the volume of the solid bounded by the graphs of the following…

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Q: Which of the following is the partial derivative with respect to x of the function f(x, y) = 2y sin…

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Q: f(x, y) = Find fx, fxy, and fxyx. 7 8x+5 + 8x³ e-8y

A: The given function is;  f(x,y)=7/(8x+5) +8x3/e-8y.

Q: lim cot 1 -1 8418 1

A: A detailed solution is given below.

Q: No 1 Problem Use the method of disks/rings to determine the volume of the solid obtained by rotating…

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Q: Work Problem for the question. Let You must provide a clear and detailed solution z = (y-2x)³. where…

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Q: Evaluate f cosh² x dx đ (sinh 2 từ t + x) + C O 2r O2e² +42 + C 8 O None of the choices…

A: We have to evaluate  ∫ cosh2(x) dx

Q: Let A = A(r) give the area of a circle of radius r. The instantaneous rate of change of the area as…

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Q: dy Find using implicit differentiation. dx Hint: First clear the denominator to get 8x² + 6y =…

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Q: Find f tan 0 de. ] a. C. - In sin 0+ C - In cos 0+ C sec² 0 + C - In sec 0 + C

A: Here we have to solve the integral.

Q: Activity 1. Evaluate the following definite integrals by using the fundamental theorem of Integral…

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Q: ات, 01 +19+₂1 x+₂²0 +19+₂. 1. Evaluate

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Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: The integral 2 fossin drde is equal to π/2 O-1/2 O 1/2 0 1 00 10

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Q: (x¹+y¹) dx - xy³ dy = 0 [Answer: y = 4x¹logx + Cx¹]

A: This question is based on Homogeneous differential equation.

Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

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Q: Evaluate fz² In z dz using integration by parts O² Inz-+c Onz-+c Onz-+c 2²lnz - 2 + c 12 21

A: Solution:  step-1: Evaluate ∫z2*lnz dz using integration by parts                Formula for…

Q: If f'(1) = 4, f(1) = 2, and g(x) = f(x) tan-¹x, what is the slope of the tangent line to the curve y…

A: Here we have to find the slope of the tangent line.

Q: Question a) b Let f(x, y) = x³-4xy² x²-2y Find the first partial derivatives of f. Determine whether…

A: According to question,Given Function,fx, y = x5 -4xy2x2 - 2y

Q: EV None of the choices Ocot³ (1)-cot (1) - ○tan³ () - tan() Ocot³ (¹)-tan (1)

A: givenI=∫cot4(1θ)θ2dθlet  1θ=x-1θ2=dxdθ1θ2dθ=-dxI=-∫cot4(x)dx…

Q: Given y = cos(3x), find O O 3 2- * N O √3 3√3 dy at x = 5

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Q: If y = xcosx, what is dy if x = and dx = 0.2 ? 0-1/2 0-20 05/0 O EN T 10

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Q: a b) exist. x² yesy 8x4+7y² Find the domain of the function f. f(x, y) = Show that lim f(x, y) does…

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Q: Consider the series Σ +∞ (-1)" n=1 n Which of the following statements is true? The series diverges…

A: Correct option (b)

Q: Find lim X-0 √x² + 100-10 x²

A: We will find the value of the limit in the following step.

Q: Find the limit, if it exists, or show that the limit does not exist. x² - 3y² lim (x,y) (0,0) x² +…

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Q: 01. |x2 - 1\dx = a. b. 2 C. 432 - 23 23 d. 틀-

A: This question can be solved using the concept of definite integrals and modulus function.

Q: Which of the following is not true? d dx O d dx d d.x [sech a] = sech z tanh x dx [csch a]=-csch a…

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Q: A dam has a semi-circular gate at the bottom that is 4 m in diameter. The dam is 12 m high and…

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Q: Find 7 sin (7x) dx

A: According to question,Given Integral,Let I = ∫7 sin27x dx

Q: z = (x + y)², x = s²t, y = st². Use the Chain rule to find dz for t = 1 and s = 2. ds

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Q: Find (²-1) ln(x)dx

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