A rectangle is inscribed with its base on the x-axis and its x². What are the = upper corners on the parabola y 11 dimensions of such a rectangle with the greatest possible area? Width = Height =

Q: Let f(x)= Select the correct description of the one-sided limits of f at x = 0. Choose 1 answer: lim…

A: Above question is solved.

Q: dx 8. √√√x+√x

A: We have to find out solutions

Q: Calculate the value of the following limits algebraically, (if they 2x-1 a) lim x+1 X² 2x²-9x-5 b)…

A: Topic:- application of calculus

Q: H.W: show that the equations are homogeneous and solve: 1. (x+y)dy + (x - y)dx=0

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Q: 2dx 3 X - - 2 X

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Q: √4x²(x³-5)ª dx = Ox³(x¹² - 25x¹ +250x6 - 1250x³ +6250) + c 12 15 O 16(x³ - 5)4 + c ○(x³ - 5)5 + c…

A: To evaluate ∫4x2x3-54dx Formulae used d(xn)=nxn-1d(constant)=0∫xndx=xn+1n+1+c

Q: The volume generated by revolving the first-quadrant area bounded by the parabola y2 = 8x and the…

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Q: 4. Which of the following is an exact DE? A. (x²+1)dx-xydy-0 B. xdy+ (3x-2y)dx = 0 C. 2xydx…

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Q: Find the centroid x of the plane region y=9-x^2 bounded by the positive x and y axes. O x = 3/4 O…

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Q: Find the derivative of the following exponential and trigonometric functions: please attach your…

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Q: Solve the following quadratic equations (if they have solutions) a. 15x²0 = b. 2x² +9=0 c. x² - 4x +…

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Q: What is the area bounded by the curves x = 1/y, 2x - y = 0, x = 6, and the x-axis?

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Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region above the…

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Q: Question 1 If A = sin ui + cos uj + uk, B = cos ui - sin uj - 3k, and C = 2i + 3j - k, find (A X…

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Q: 1. Show that z³+y³ lim (x, y) (0,0) 1² + y² does not exist.

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Q: f(x) = 3x² - 5x+21

A: SOLUTION-

Q: x and y are functions of a third variable t. If √√x + √= 5 and dt = 2, find when = dt 1

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Q: lim (SC - S(T)) where f(x) = -x²+x+6 f(7+h)-f(7) h h→0

A: f(x)=-x2+x+6= limh→0 f(7+h)-f(7)h limh→0 -(7+h)2+(7+h)+6-[-72+7+6]h limh→0…

Q: Given f(x): 5x² 6x +13, find f'(x) using the limit definition of the derivative. f'(x)=

A: Given problem:- Given f(x)= = 5x²-6x+13, find f'(x) using the limit definition of the derivative.

Q: Find the regions where sinx sx.1

A: Topic:- trigonometry

Q: f(x) = 120x0.80

A: You must have an idea about basics of derivative in order to understand this problem.

Q: The 33-N force P is applied perpendicular to the portion BC of the bent bar. Determine the moment of…

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Q: Betermine the value of k for which the following planes are perpendicular: π₁ = (1, 2,7) + s(4,2,0)…

A: π1 = (1,2,7)+s(4,2,0)+t(k,1,2)  First need to find the normal of the planeIf the plane in the form…

Q: The value of (-1+√3 i)^(1/3) is О 2 exp((2TU/7)^i ) 2 exp((2/3)^i) 2 exp((2T/9)^i) 2 exp((2T/5)^i)…

A: We need to choose correct option. As per Bartleby's guidelines we can solve only one question from…

Q: solve the differential equation for initial value problem using the method of undetermined…

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Q: Use a double integral in polar coordinates to find the volume of the solid bounded by the graphs of…

A: Concept: Polar coordinates are  x=rcosθ , y=rsinθ Now adding the square of both the equation…

Q: hand written pl Let A(0,-2), B(0,4) (1) Find the set of all points P(x, y) such that m(PA) 2. m(PB)…

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Q: Find the constant a such that the function is continuous on the entire real line. f(x) = √5x², x ≥ 1…

A: We need to find a.

Q: a. Find the lengths of the sides of a rectangle whose perimeter is 40 cm and whose area is 75cm².…

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Q: Find the volume of the solid generated if the area bounded by y = = and the x-axis from I x=1 and…

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Q: Differentiate the function with respect to the independent variable. x f(x) = 4x cos+ + cos f'(x) =…

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Q: Evaluate: lim 1+ O 1 a 00 none of the choices In aª (A)

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Q: iii please, NOT i or ii

A: Topic:- vector algebra

Q: Deriving the formula for volume generated by revolving the first- = quadrant area bounded by the…

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Q: integrate [(x csc^2 (2x) - x cos (2x)] dx

A: Given problem:-  ∫ [(x csc2(2x) - xcos(2x)] dx

Q: 2. The base of a solid is an ellipse whose major axus and minor axis are 12 cm and 8 cm long,…

A: We need to find volume.

Q: S 3x+1 -dx x²-x-6 2

A: We know, ∫ dx/x = ln|x|

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Concept: Exact differential equation: For the differential equation of the form Mdx+Ndy=0 If ∂M∂y=…

Q: Suppose that x² + y² = 82. dy (1) Use the method of implicit differentiation to find dx dy dx (2)…

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Q: H.W: Given the following table find x3, fo Af₁,Af₂, A² fo j xj Afo A² fo 0 fo 30 A² fo 4 20 Af₁ 2 14…

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Q: y= x² +9

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Q: 2x-x² dx

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Q: Integration of { 8t^7dt

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Q: Find the total number of permutations of the word 'ASSASSINATION', where all vowels are ALWAYS…

A: We have to find the number of ways

Q: Determine if the function f(x) is continuous and/or differentiable at x = 5? x+5 for -5≤x≤5 f(x)= 2x…

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim (5x - 7) X→-6

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x² + 3x lim x-3 x² - 4x…

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Q: 9. Brett and Julia are getting married and the menu options at the wedding are as follows: Main…

A: Above question is solved.

Q: Solve the differential equation for initial value problem using the method of undetermined…

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Q: 1. f(x) = 4x² (8x + 1) 2. f(x) = (100x² + 25x)(10x² − 15x) 3. f(x) = (2x + 1)(4x + 3) (5x - 1)

A: Let's solve all given derivative by using product rule.