1. Evaluate the definite integral *2³²√³+1 dr. (a) ² (27+2√2) (b) (27-2√2) (c)(2√2-27) (d)/(2√2+27)

Q: Assume that f is continuous on the set of real numbers. Find a and b given that b 3 [ f(x) dx - f₁…

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Q: Find the net signed area of ƒ (x) = x - 2 over the interval [0, 6], illustrated in the following…

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Q: Lets a real constant such that s ≥ 0 in the process of calculating = 1,500 3.1 di you get: O a) I =…

A: s real constant such that s≥0I=∫1+∞x-3.x-sdx

Q: Q2A)Matrix 4 = [],find Eigen values of 4². A

A: The given matrix is  A= 1342. We have to find eigenvalues of A2. Eigenvalues are the roots of the…

Q: 2. Evaluate 6x²e4x³ dx.

A: Let 4x3 = t

Q: 11.Sketch the graph of the region D and evaluate the double integral y dA, D = {(x,y)| 0≤ x ≤ ¹,0 ≤…

A: The region D is bounded by the below curves:x=0 to x=1; y=0 to y=x3.

Q: (a) Find the average value of f(x) = 25 - x² on the interval [0, 2]. Answer: (b) Find a value c in…

A: SOLUTION-

Q: If f is the function given by ƒ(x) = √²* √t² — t dt, then ƒ' (2) = 7 a. 2√12 b. √2 c. √12 d. 2√12 B…

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Q: At point (1,-1,2). 4

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Q: B)Evaluate the integrals: i) f/2 inzerdrde " 0 ii) f/25/2 sinx 2² siny dz dy dx. π/2

A: B.1. According to question,Given Integral,Let I = ∫0π2∫0sin 2θr dr dθ

Q: Evaluate the integral. 2 - 121 y - 121 2 -dy, y> 11 dy=

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Q: I(X) {(-2,1), (1,4), (2,5), (3,6) g(x) = 6 + 4x h(x) = -x² + 2 2. 2h(3)+g[f(-2)] find 1. h[f(1)] 7…

A: 1. hf17=h47                  =-16+27                   =-147                    =-22.…

Q: Question 1. A critical point of the function g(x, y) = ex y + 3x²y-y is (0,0). Use the Second…

A: Explained below

Q: 5. Integral ReR dR

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Q: The number N of Netflix subscribers in Grassyboro is shown in the table below. Estimate the…

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Q: Q3A)Find normal line and parallel plane to the function f(x, y, z)=x²y²z²-4 At point (1,-1,2).

A: To find normal line and parallel plane to the function fx, y, z=x2y2z2-4 at point 1, -1, 2.

Q: Find the general solution of the following differential equation. y" - 11y' + 18y = 0 NOTE: Use c₁…

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Q: Use the formula for the area of a trapezoid to evaluate √₂² (2x- 2 (2x + 3) dx.

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Q: Solve the given differential equation. 16x2y" + 16xy' - y = 0 C₁ cos(In(x)). + C₂sin (In(x)) 4 4…

A: here we have to solve differential equation.

Q: A) Find area bounded by y = 0, y = √x - x² using double integration.

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Q: Question The graph of f(x) = -2x³+x-3 is shown below. Use the tools to graph the line tangent to…

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Q: Which of the sequences {a} in Exercises 31-100 converge, which diverge? Find the limit of each…

A: For the given sequence, If limit of the sequence at n -> infinity finitely exist, then we'll say…

Q: Find dy/dx by implicit differentiation. 19) x3 + y3 = 5 20) 2xy-y2=1

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Q: Evaluate each integral. √x+Yy dz Jx - "X rx + y 0 Jx-y y dz dy Now evaluate J = = y dV, where E =…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 4…

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Q: B. Given that f(x) = {(-2,1), (1,4), (2,5), (3,6)} g(x) = 6 + 4x h(x) = -x² + 2 find

A: given

Q: Consider the functions f (red) and g (blue) y 10 12 for these functions we have that the line y=8 is…

A: Topic = Limits Just 1 is true.

Q: p(x) Given the Rational Function f(x) = q(x) Assume the numerator and denominator have no common…

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Q: ( (tano-1)² do

A: Given ∫[tanθ-1]2 dθTo evaluate the integral:

Q: Show that there are no tangents to the curve f(x) = 6x3 + 2x2 that have a slope of -5.   Please…

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Q: the complex number 6√3+6i in polar form 12(cos(n/6)+isin(n/6) 12(cos(n/4)+isin(n/4)…

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Q: What is the polar equation of a circle of radius a centered at the origin? Use this equation to…

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Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

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Q: Use the method of reduction of order to find a second solution of the differential equation ty" +…

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Q: Write an equation for the function graphed below. The y intercept is at (0,-0.3) 5 4 3 2 1 + -6 -5…

A: We have to write an equation of given graph.

Q: 4: Find the indefinite integral of f(u) = -1-3√ =

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Q: Problem 1. Solve these integrals using substitution (a) x(x-2)³ dx, (b) text² di dt.

A: The given integrals:a∫xx-25dxb∫te3t2dtWe will solve them using substitution.

Q: Find the minimum and maximum values of z=6x+7​y, if​ possible, for the following set of constraints.…

A: The given constraints are: x+y≤9-x+y≤32x-y≤12

Q: 11. Draw a high-quality graph by hand on graph paper for the function f(x) = 2x³ + 6x². Your work…

A: Given :  f ( x ) = 2x 3 + 6x2  find minimums , maximums and inflection points ,  And intercepts

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Find the general solution of the following differential equation. 4y" +36y' +81y = 0 NOTE: Use c₁…

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Q: 1. Find the area bounded by r = cos 0 for -π/2 ≤ 0 ≤π/2. 2. Find the length of the r(t)= , 1≤t≤ 5 3.…

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Q: How much money should David invest today into a fund that earns interest at 3.50% compounded…

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Q: Question 8 Find the partial derivative of z with respect to x None of the choices dz (2r−y) да…

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Q: 2) By using Lagrange multiplier method, find the maximum value of f(x, y, z)=x+ z subject to the…

A: Given function:-     f(x, y, z) = x + z subject to condition x2 + y2 + z2 = 10

Q: Assume x and y are functions of t. Evaluate dy/dt. 12) x3+y3=9;- dx dt 13) xy + x = 12; dx dt = 4, x…

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Q: Solve the initial value problem y" - 2y' — 35y = 0, y(0) = a, y'(0) = −10. Find a so that the…

A: Here we have to solve the differential equation.

Q: Q1A) The vectors A = 3i + j + 4k, B = 2i - 3j - k, find vector normal to A and In plane of A and, B.

A: Solution is given below:

Q: Find the average value of f(x) = x² on the interval [2, 4]. Answer:

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Q: Evaluate the integral using integration by parts. Scot-¹(8y)dy 1 Scot ¹(8y)dy = -x In (cos (6y)) + C

A: The given integral,       ∫cot-18ydy