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Q: Assuming that the equation below defines y as a differentiable function of x, find the value of…

A: Using differentiation

Q: By using double integrals, find the surface area of the portion of that lies inside the cylinder x²…

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Q: dy 7. a) Prove that, fo-y4 = 4√/2n e2x b) Prove that, √∞ (e³x+1)² dx: = 2π 9√3

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Q: find the integral sinh sinh?(5t)cosh?(5t) dt

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Q: Compute the derivative of f(x) = e^x/ x^n for constant n using the specified methods: (a) The…

A: Use the product rules of the derivative is d/dx(uv)=u*(dv/dx)+v(du/dx) And quotient rulesd/dx…

Q: If f(x) = 2x + x ² = O 4.155 O 5.155 O 12.464 O 13.164 2x + x2, what is the average value of f(x)…

A: The given function is; f(x)=2x+x1/2, [0,3]Find the average value of the function.

Q: In a study of factors that influence brand switching by a certain demographic, the following factors…

A: Since, you have asked a question with multiple subparts, as per company guidelines we will solve the…

Q: 10. The position of an object moving in a straight line is given by: S(t) = -2t³ + 5t² - 10t +20 (S…

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Q: Find the derivative of the function f(x), FIRST using the Product Rule & SECOND Quotient Rule.…

A: The Product Rule:The Quotient Rule:The Chain Rule:The Power Rule:

Q: Find the four second partial derivatives of the following function. 5x z = 8ye

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Q: Differentiate but leave your answers in unsimplified form. a) y = 5x³ 4x-² +6 c) y = √x² + 3x b) y =…

A: We know that the derivative of x^n=nx^(n-1)

Q: For what value of the number k is the following function continuous at r=2 if x 2 f(x) = = (A) 3…

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Q: M 12 M Let p(x) = x³ – 5x² + 4x − 20. Verify that p(5) the other roots of p(x) = 0 over the complex…

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Q: Given the initial condition y(0) = 2, find the particular solution of the equation e'y' - 2x = 0

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Q: State the domain for the function f(x) = In(x + 2) : O (-00, -1) O (-∞, -2) O (-2,00) O (-∞0,00)

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Q: Find the volume of the tetrahedron shown using the order dz dx dy. The tetrahedron is bounded by the…

A: The tetrahedron is bounded by the planes Now, from above data limit of z is:-Now, we need to find…

Q: , find the range of the function f(x) = 2x² + 12x – 3.

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Q: The graph of f(x) is shown along with the line y = x: Assume that f-1(x) is defined by restricting…

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Q: Sex sin⁹⁹⁹ (e*) cos³ (ex) dx

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Q: 25. Determine the value of k so that f(x) is continuous. Show work. x² - k f(x) = 2x² + 7x - 22 x≤2…

A: given function is

Q: Find the maximum value of ƒ(x, y) = x¹y³ for x, y ≥ 0 on the unit circle. fmax =

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Q: Use a graphing utility to (a) plot the graphs of the given functions, (b) find the approximate…

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Q: 25. Determine the value of k so that f(x) is continuous. Show work. x² - k 2x² + 7x-22 x≤2 x>2 x-2…

A: A function f(x) is said to be continuous at a point a, if Left hand limit and right hand limit and…

Q: By considering different paths of approach, show that the function below has no limit as…

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Q: Find the Volume V(S) of the solid S generated by given R: R is the region bounded by x²+y-4=0 and…

A: To find the volume of the solid S generated by revolving the region R about the line x=-2, we can…

Q: If f(x) = 3x-2 and g(x)=x+1, then (f(g))-¹(a) equals 01-2 O (3-1) O x-1

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Q: 1. Compute the given quantity: ∫∫(2xy)dxdy for x over the interval (0, 2) and y over the interval…

A: To compute the given quantity. for  over the interval  and  over the interval .Note: Since the…

Q: dw Use the Chain Rule to find where w = sin 8x cos 2y, x=, and y=t4. dt dw dt (Type an expression…

A: Using to chain rule :

Q: Evaluate the line integral Jc (2x³y³) dx + (9x³ + y³) dy where C is the unit circle, and verify…

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Q: 21. a) Evaluate the following limits. Show proper steps. 8x²-2x-3 2x+1 a) lim x→→ 2 2x x-0 √2x+1-1…

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Q: Suppose that h(x) is an unknown function with the following properties: ex x² ● h'(x) - h(1) = 3 Use…

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Q: Find the first partial derivatives for f(x,y) = 3x cos (xy). =0

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Q: if f(x)= xe^x, determine f^(400) (x)

A: To determine the 400th derivative of the function f(x) = xe^x, we can follow a systematic approach…

Q: e) Plane that is parallel to the xy-plane that contains the point A(2, 1, 3) (ca

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Q: 2. A waterwheel with radius 7m, has 1m submerged. The wheel rotates at 6 revolutions per hour. Time…

A: waterwheel

Q: 1. у ул y=3x - x² 0 y=x (2, 2) AX

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Q: Below is the graph of a function. Which of the following could be a graph of its c 3 2 1 -2 T3/ 1 2…

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Q: 1. Consider the following vectors a = [1, 3, 2] & b = [-2, 2, 1] a. Draw each vector on a grid b.…

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Q: 5.4 Find the first partial derivatives of f(x, y) = 4x³y² +9x²y + 10. af Əx 11

A: given

Q: 2. Determine the absolute maximum and minimum values of f(x) on the interval -2≤x≤05. Decimals…

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Q: For the following lines: L₁: x =− 3 + 3t, y =− 1 + 4t and L₂: 2 a) Determine the point of…

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Q: 1. Find the polar coordinates, - ≤ 0 < 2π and r ≤ 0, of the following points given in Cartesian…

A: According to bartleby guidelines we supposed to do the first three of multiple subpartskindly repost…

Q: - Q1. Consider the function f (x) = − tan(x − π). a. Determine f '(x). b. Determine the slope of the…

A: Consider the function (a) To determine .(b) To determine the slope of the tangent to the curve  at…

Q: Let R(x, y) = 0.7x³y² -5x³ +6y², find the second partial derivatives: a²R oy²

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Q: 5 x√x-1 dx

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Q: 5. Let f(x) = [2-kx k+x with the value of f(1) to be determined. (a) Compute lim f(x) in terms of k.…

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

Q: Using the graph above, evaluate the following limit. lim f(x) (A) 1 (B) 2 (C) 3 (D) The limit does…

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Q: 3. True/False. Indicate whether each statement is true (T) or false (F). a) b) The derivative of a…

A: To indicate whether each of the following statement is true (T) or false (F).(a) The derivative of a…

Q: 6. Determine the point of intersection between the graphs f(x)=2(3)²x-1 and g(x)=3(2)³x

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Q: 6. The function f(x) is defined by the graph. State the value of each: a) lim f(x) = b) lim f(x) = x…

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