Define the binary operation in the set of rational numbers as: a*b = ab + a-b Which of the following properties is satisfied? 1. Closure Property II. Commutative Property III. Associative Property O I only II and III I and II O I, II and III

Q: A 30-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1…

A: We have to find the limit.

Q: Suppose f(x) = 3x² + x - 3x²+x-6. Compute the following: A.) ƒ( − 4) + ƒ(1) = = B.) f(-4)-f(1) =

A: Given f(x)=3x2+x-6f(-4)=3(-4)2+(-4)-6=3(16)-4-6=48-10∴f(-4)=38

Q: PO: Given the surface 2 cos xexây 5 y a) find of the question of the tangent plane to the surface…

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Q: Use a linearization to approximate tan(π/100).

A: This question can be solved using the concept of linear approximation.

Q: Correlational designs have one independent variable and one dependent variable  true or false?

A: Explanation:-  A  dependent variable is the variable to be explained and independent variables are…

Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a<b means that a…

Q: 9+xn 5n n=0 An empty set since the series diverges Find the domain of ƒ(x) = Select one: O (-1,1) O…

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Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: Evaluate using Partial Fraction Decomposition: S x² (x+1)²(x-1) dx

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Q: nverse for the following functions. If it does not exist, show why. f(x)=2x-1 f(x)=√x-3 f(x) = |x-1|…

A: Topic:- calculus

Q: Q3) Determine the maximum point of the function f(x) = x(5-x) with Fibonacci search method, if the…

A: Here, we have fx=x5π-x. The number of experiments to be performed are n=4 and the first uncertainty…

Q: f(c) {}} [=+3 = < (3x + 1

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Q: Determine the area of the region bounded by the curves y = ₁, y = 2x and x = 4

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: Find a plane containing the point (-3,-3,5) and the line x(t) y(t) z(t) = = 8 + 4t -4-6t -7-3t

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Q: П 2 0 KIN 2 p² sinr de dr dø 0

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Q: Determine if the improper integral is convergent or divergent?

A: The given integral:∫e∞1xln7x dxWe need to check whether the improper integral converges or not.

Q: Iff and g are differentiable functions and h(x) = f(x)ex) , then K'(x) = rosen Fixe+fixie O [00+0000

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Q: Given the function f(x) = -2x + 6x within the interval [0,8], at what values of x do the absolute…

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Q: Solve the integral shown below. JT fsins 2x cos7 2xdx

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Q: 4dx x- 3√x²

A: Evaluate the integral

Q: Find the Volume: Rotate the region bounded by y = √x, y = 3 and the y-axis about the y-axis

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Q: A small metal bar, whose initial temperature was 30° C, is dropped into a large container of boiling…

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Q: wal u a Write the vector shown below as a combination of vectors and 7 shown above. a Vector - 21+ V…

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Q: Determine whether the differential equation (2x² − 2xy + 3) dx + (7y² − x² + 2) dy = 0 is exact. If…

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

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Q: * Two unlike parallel forces, each of magnitude 50 kN are 200 mm apart from each other. what will be…

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Q: 4dx 3r x-√√x² S

A: Let's solve given integral.

Q: (d) Find the mass of lamina enclosed by y = ax² and y = c if the density of lamina d = xy a-2 c-6…

A: Let's find mass of lamina(m).

Q: Q2. If f(x, y) = xy² + y²cosy + xsiny then a) y² - siny c) 2y + cosy a²f is дудх b) y² + cosy d) 2y…

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

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Q: Solve the following x³-x²-√√2x limx→2²-11x+18

A: Above question is solved.

Q: f(x csc² 2x − x cos 2x)dx

A: Given problem:-  ∫(x csc2(2x) -x cos(2x)) dx

Q: Find the point at which the line x(t) y(t) z(t) - 5+ 5t -6-8t intersects the z plane. - 7+8t

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Q: A car is moving with uniform acceleration. it covers 200 m in 2 sec and 220 m in next 4 sec. the…

A: A detailed solution is given below.

Q: A person is standing between two cliffs. A sound is produced, the person hears echo after 3 seconds…

A: Let the distance between the two cliffs = (a+b) m Speed of sound = 332 m/s

Q: dy dx If y = (sin x)¹/, then (sin x) ¹/x In(sin x) x² (sin x) ¹/x x - ln(sin x) x² x cotx - In(sin…

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Q: E) If F(x, y, z) = 3x²i + 3zj - 3xk find the Div (Curl F). 0/0 0/0 0/0= az any jaz V-Vx3 = 0₂ 17 Pue…

A: First we find curlF .

Q: f(x csc² 6x-x cos 6x)dx

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Q: (a) Find where x² + 3xy + y² = 3 at (√3,0). da

A: topic- implicit differentiation

Q: Identify the number of significant figures (sig figs) in each of the values. I sig fig 2 sig figs 3…

A: We can find the significant figures.

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: . Consider the signal f(t) 0, -1 ≤ t < 0; 1-t, 0≤t≤ 1. This signal is periodic with period 2. (a)…

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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: 4x² + 4y2 +422-8x + 16y=1 presents a sphere, and find its center and radius.

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Q: Sketch the graph of a single function f(x) that satisfies all of the following conditions, labeling…

A: The function satisfies the condition,The domain of fx is -∞,∞f'x=5x2x2-3f''x=10x2x2-3f0=0

Q: Find the derivative of the function 6. g(s) = f (t – t²)³ dt 5

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Q: A stone is released with zero velocity from the top of a tower, reaches the ground in 4 sec. The…

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Q: If dx = e-²y and y = 0 when x = 5, then the value of x when y = 3 is dx e6 +9 A. e5 C. 2 B. e6 + 1…

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Q: (e) If f and g are differentiable then, d 1 f(g(x)) = f'(g(x))g'(x) dx True False

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Q: Nx - My M If = Q, where is a function of y only, then the differential equation M + Ny' = 0 has an…

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