Find the first partial derivatives of the function. Əw ди Əw Əv 11 || W = ev u+v7

Q: Find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the…

A: The parametric equations are given by The point is

Q: Find the area of a triangle PQR, where P = (0, -1, –4), Q = (6, 5, -2), and R=(-6, 6,-5)

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Q: Estimate I = 5 3 · [° ( ²1 + ³) X (a) Left endpoints. I≈ (b) Right endpoints. I≈ + 3) da using n = 4…

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Q: 9 Find the center of mass of a thin plate of constant density & covering the region bounded by the…

A: Find the center of mass of a thin plate of constant density  covering the region bounded by the…

Q: Evaluate the integral in terms of the constant: S₁x²¹ dx = 4 4 ←|

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Q: Use differentials to estimate the maximum error in the volume of a rectangular box with square base…

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Q: Find the volume of the solid bounded by the coordinate planes, the plane y = -2x + 2 and the…

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Q: Find y'' if y = 2x sin x. O O O A. y'' = 4 cos x - 2x sin x B. y'' = - 2x sin x OC. y'= - 4 cos x +…

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Q: Let u = Compute the following: ū• v = (1, −5, −1) and v = (-5,2,0). v.u ||ū|| ² - 3 (u.v) (-3ū) v =…

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Q: vings of soda. One serving of energy drink contains 42 mg less caffeine than one serving each of…

A: Let the amount of caffeine in one serving of coffee; energy drink and soda are x,y,z…

Q: Find the time required for an investment of 5000 dollars to grow to 6500 dollars at an interest rate…

A: To find the time required for an investment of 5000 dollars to grow to 6500 dollars at an interest…

Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. lim 00+u n √…

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Q: Find the smallest perimeter and the dimensions for a rectangle with an area of 49 in². The smallest…

A: Let the dimensions of the rectangle is denoted by x and y As we know that area of the rectangle is…

Q: Use Ayf'(x) Ax to find a decimal approximation of the radical expression. √/63.35

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Q: A homeowner wants to enclose three adjacent rectangular pens of equal size along a straight wall, as…

A: Consider

Q: Solve ABC subject to the given conditions A= 10.5° , C=97.8° , b=61

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Q: Find the equation of the plane containing the point (-5, 5, -6) and parallel to the plane -2x- -y-4z…

A: To find the equation of a plane containing a given point and parallel to another plane, we can use…

Q: The Pacific halibut fishery has been modeled by the differential equation dy = = ky( 1 - 1 /1) dt…

A: The integrating factor of this equation is,Therefore,putting the value of u in terms of y,Given at t…

Q: Three towns are located at 3 spots denoted by the Cartesian coordinate system. c (-5,2) A (3.10) B…

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Q: Find the zeros of the function, and their multiplicities. f(x) = x³ +7x² -x-7 The smallest zero is…

A: Note that as per the rules we are supposed to answer the first question and rest of the questions…

Q: On the xy-plane, let D be the rectangle x = [−2, 3], y € [0, 80]. Evaluate the double integral I =…

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Q: Graph the polynomial function. Use synthetic division and the remainder theorem to find the zeros.…

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Q: The curves 7₁(t) = (6 sin(t), 8 cos(t), eª) and 7₂(t) = (2 ln(t), 8√t, t³) intersect at the point…

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Q: Use a graphing utility to graph the curve represented by the parametric equations. (Indicate the…

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Q: Find the indefinite integral. (Remember the constant 8 / (√x + = - Sex) dx X

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Q: dentify the inflection points local maxima Local minima? What are the intervals of concave up?…

A: In this question , we will find the concave up or down and inflection point.

Q: The equation of the tangent line to a function fatxa is given by the equation y = 4(x-a)+b. Use this…

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Q: Find the absolute minimum and absolute maximum values of the given functions in the indicated…

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Q: Determine all critical points for the following function. f(x) = 2x(16-x)³ X= 3 (Use a comma to…

A: Let a function denotes by f( x ) then its critical points can be find as Given function

Q: If g(x)=xf(x), where f(3) = 4 and f'(3) = -2, find an equation of the tangent line to the graph of g…

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Q: To save money for a future house, a couple places $4,000 in an interest bearing savings account…

A: Here, Principal amount (P) = $4000 Interest rate (r) = 9%  or 0.09 The amount is compounded monthly,…

Q: Consider the function Evaluate the definite integral. х f(x) = { { 1 M/S 3 S³ if x < 1 if x ≥ 1 f(x)…

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Q: f(x, y) = 2x³ – 6x + 6xy²

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Q: (5) Let f(x) = = x² 2-x ; x ≤1 ; x > 1 Consider whether f is continuity at x = 1 or not?

A: Given: To Find: To determine whether  is continuous at .

Q: 2. Create a matrix expression that represents a 90°clockwise rotation of v reduced by Calculate the…

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Q: Calculate the iterated integral. [[³² dy dx 4xex y

A: The integration,

Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

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Q: (e) tan(sin−¹ y) = √2, y € (-1,1)

A: To prove"As per the rules, we are supposed to answer the first question and rest of the questions…

Q: Find the unit tangent vector to the curve defined by F(t) = (2 cos(t), 2 sin(t), 5 sin² (t)) at t…

A: r(t)=&lt;2cos(t),2sin(t),5sin2(t) &gt;Find unit tangent vector at pi/4.

Q: 3. Use the Laplace transform to solve the Initial Value Problem x"-x'- 6x=0; x (0) = 2,x'(0) = -1

A: given initial value problem

Q: The slope of the curve y = - 10x² at (-1,-10) is. (Simplify your answer

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Q: If f(x) = then f"(x) = = X √ ² ( 2³ + (t³ + 4t² + 5) dt 0 ←

A: Let,Using integration formula So,If  dtPut , dt = F(t)Then So,

Q: (11) Fine lim f(x) when f(x) x-0 = 0; X = 0 2; X = 0 (Ans. 0)

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Q: 22.Determine the points of inflection for the function: g(x)=x+2cosx. ㅠ 114 ② 66 ㅇ 플 ® 0, 7,27 D ㅠ3ㅠ…

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Q: Given the vector-valued functions u(t)=e5t+e²t + 2tk v(t) = 4ti + t²j + 4k d find (u(t) · v(t)) when…

A: We need to find derivative of dot product at given value.

Q: Find dx = dy for y = dx cot x 1 + cot x

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Q: Find the location at t = 3 of a particle whose path satisfies dr = (18t - (12,21-4) dt + r(0) = (12,…

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Q: Find the indefinite integral. (Use C for the constant of integration.)

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

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Q: For the demand equation, use implicit differentiation to find dp dx p² + p + 8x = 120 dp dx ||

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