Use the cross product to find the area of the parallelogram whose vertices are (0,0,0) , (0,2,1), (2,4,3), and (2,6,4).

Q: Convert the rectangular coordinates to polar form (√8,√8) (4,57) (√2,73) Option 4 O Option 1 (2,3)…

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Q: Calculate the following antiderivatives: (a) ∫ 8t− 6t^6 −5dt =  +C. (b) ∫ 1/u^7/4 + 3.5 sqrt u du…

A: a) Given:       ∫8t-6t6-5dt  =∫8t dt-∫6t6 dt-∫5 dt taking constant out     =8∫t dt-6∫t6dt-5∫ dt…

Q: 5) Find the slope using y = (=/3² at 2 First Principle (-3,8)

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Q: Evaluate the definite integral. 2 cot-¹(x) 1 + x² 1 - 1 dx

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Q: 7 lim X-DO 11 Find the limit sin (7x) x

A: To find the following limit.limx→0 sin7xx

Q: 1 a. Determine whether the Mean Value Theorem applies to the function f(x) = x + on the interval…

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Q: Let f(x) = be a piecewise function. Evaluate So fo f(x)dx= 3x²+2, 2x - 3, if x < 2 if x ≥ 2

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 15 – 2t, where 0 ≤ t ≤ 3…

A: Here, the displacement is: S(t)=-t2+15t

Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable.   lim x→∞…

A: The given limit,      limx→∞1+axx, for some constant 'a'

Q: J (2) Ten thousand dollars is invested at 645 intrest Compound Continously. → when will the…

A: We can find the required time as below.

Q: Represent the plane curve by a vector-valued function. x² + y² = 36 r(t) = (No Response) Need Help?…

A: The plane curve x2+y2=36

Q: (a) Verify that y=tan(x + c) is one-parameter family of solutions of the differential equation y'= 1…

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Q: Problem 2. Find the area between these curves: (a) f(x) = 5x-2 and g(x) = 4x + 1 on the interval…

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Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

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Q: Convert the rectangular equation to polar form x² + y² = 9 (solve) rsin0 = 9 r=4.5 Option 4 O Option…

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Q: Solve the equation. dx 2x1² dt **** An implicit solution in the form F(t, x) = C is =C, where C is…

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Q: (a)i- Show that the following equation represents a sphere, and find its center and radius.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Problem3 Find a curve in the xy-plane passing through the point (1, 2) and for which the normal line…

A: Here we have to find the equation of curve.

Q: Consider the following functions. f₁(x) = x, f₂(x) = x², f3(x) = 4x2x² g(x) = c₁f₁(x) + c₂f₂(x) +…

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Q: Find a bif a= (4, - 1,5) ar . b = (-3, 8, 5).

A: Here we will find whether given vectors are orthogonal or not,

Q: The Eigen value of matrix p is (solve) ГО 0 Lo 1 0 0 1 -3 -4] (0,-1,-3) O (0,2,3) O (0,1,3) O…

A: This question can be solved using the concept of matrices and determinants.

Q: Evaluate: 10 sin(3x)dx None of them -0.532 -0.253 0.253 -0.235 0.0235 -0.325

A: The given integral is:∫π6π4sin3xdxWe need to solve the above integral.

Q: Evaluate 2 6 (x + 2)√√/x-2dx

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Find the following for the given equation. r(t) = 8 cos(t)i + 8 sin(t)j (a) r(t) = (No Response) (b)…

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Q: Given the curves y=(x^2)/2​  −4·x and y=−x^2+8,   Sketch both curves on the same coordinate plane…

A: Let's solve.

Q: The definite integral is equal to Select one: lò xác thỉ xác Of xdx + ² xdx Of xdx + xdx Of xdx -f²…

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Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: 29 + i√/1159 6

A: We can convert the given complex number in fractional form to decimal form by calculating the square…

Q: E Surface integral is used to find Density Area Surface Volume

A: Surface integral is used to find

Q: Find the Taylor series centered at c = -1. 7 3x-2 f(x) = Identify the correct expansion. ∞ 3" - 7 Σ…

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Q: Problem3 Find a curve in the xy-plane passing through the point (1, 2) and for which th normal line…

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Q: im →0 In[(x + h)² + 1] + ln(x² +1) h

A: Given: limh→0lnx+h2+lnx2+1h

Q: * Convert the polar equation to rectangular form r=7 (solve) x² + y² = 7 x=7 O Option 4 x² + y² = 49…

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Q: Solve the differential equation by variation of parameters. y" + 2y + y = et In(t) y(t) =

A: The given differential equation is; y''+2y'+y=e-tln(t).

Q: determine the interval of increase (in interval notation) b) determine interval of decrease

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Q: Let [ 13.5 f(x) dx = 8, 45 f (a) f(x) dx = 3 J4.5 9 (b) (5f(x) - 2) dx = J4. f(x) dx = 3, and Enter…

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Q: Let f(x)=(3x(^2) -4x+5)(^100) -((2x+1)/(x-3))^5. Calculate df/dx

A: We can find the derivative as below.

Q: In a triangle ABC, a = 10, b = 12 and C= 40°, find c. - (Use cos 40° = 0.766) (Round the answers to…

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Q: 2x et. Vi-eza ex fer.

A: ∫ ex1-e2xdx=∫1-u2du=∫1+cos2v2dv=12·∫ 1+cos2vdv=12∫…

Q: Do the first two terms of the Taylor series by hand where X_0 = 1

A: Given :∫1232xe-xdx

Q: (a) Find a vector equation and parametric equations for the line that passes through the point A(5,…

A: We have to find solution for given questions.

Q: an+1 Suppose that an Σ an( – 36)" x2n n=1 → 1 as n → ∞o. Find the radius of convergence.

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Q: Is W a subspace of the vector space? If not, state why. (Select all that apply.) W is the set of all…

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Q: Two particles travel along the space curves r(t) and u(t). If r(t)and u(t) intersect, will the…

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Q: xex dx 3. f. (1+x)²

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Q: The graph of f is shown in the figure to the right. Let A(x) = for f. Evaluate the following area…

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Q: Consider the function f(x)=√/2x-8 for the domain [4, co). Find f(x), where f¹ is the inverse of f.…

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Q: Find all solutions to 2 sin(0) 0= = - - 1 on the interval 0 ≤ 0 < 2π Give your answers as exact…

A: We can find the answer as below.

Q: Find the amplitude, period, and phase shift of the function. =I 1 sin (3x-x)+3 Give the exact…

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Q: a 3. Sketch the graph of +₁ f(₂)=1₁ continous function & $²(2)=0, the point (2,1) is 2 £ is…

A: Let's solve.