Find the speed over the path r(t) = (e¹-4, −5, 4t¯¹) at t = 4. (Use symbolic notation and fractions where needed.) v(4) =

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Q: Calculate Dot Product Let a = and ☎ - - Find k so that a and k = . will be orthogonal (form a 90…

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Q: 4. Find the general solution to the DE 2x²y + xy'-3y=0.given that y₁=- is solution.

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Q: f(x) = sin 7x; л 2п Select the correct choice below and, if necessary, fill in the answer box to…

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Q: 1. Evaluate each definite integral (Hint: very few calculations are required for these problems, a…

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Q: Find the maximum value M of f(x, y) = x³y³ for x ≥ 0, y ≥ 0 on the line x + y = 2. (Use symbolic…

A: Given that fx,y=x5y3  ,x≥0,y≥0 To find : Maximum value on the line x+y=2Solution :we know that…

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Q: Find Vectors and Perform Vector Operations in R³ Let à = i + 27 + 3k. Find ||a||.

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Q: 2. lim (x, y)→(π/2,0) cos y + 1 y - sin x

A: Given query is to find the limit of the expression.

Q: x x +4 Give exact answers (not decimal approximations). Let f(x) = Find the values of where f'(x) =…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

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Q: Understand Properties of the Cross Product Find the Vector Orthogonal to Two Given Vectors Need a…

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Q: d²y(t) dt2 dy(s, t) Differential Equations + y(t) dy(t) — 2y(t) = 4x(t) - y(s, t) = dx(s, t) Linear…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: from the point (-2,-40) to the point (2,40), you'd have to compute where a = b= and f(x)= = y = 3x³…

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Q: Solve y" + 2y' - 3y = 1 + xex O y = C1e^-3x + C2e^-x + (1/8)x^2 e^x - (1/16)xe^x - 1/3 O y = C1e^-3x…

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Q: can be written in differential form: where M(x, y) = y − 3y³ = (y² + 4x) y M(x, y) dx + N(x, y) dy =…

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Q: y" - 2y + y = ex/x4 O y = C1e^x + C2x e^x + (e^-x/6x^2 O y = C1e^x + C2x e^x + (e^x/6x^2) O y =…

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Q: Write Equations of a Plane in Space Find the equation of a plane through the points (1, 2, — 7), ( –…

A: The objective of the question is determine the equation of the plane.

Q: The shaded region in D = 4 cos and lies inside the polar curve r outside the polar curve r = cos 0.…

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Q: 1. Exponential growth and decay can be expressed as A(t) = Apekt, where A(t) = the amount at time t…

A: if  k>0   ,  Exponential growth k,0   , Exponential decay

Q: Given the demand function D(p)=√√375 - 4p, How many products will be sold if the price is $2? Find…

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Q: If a and h are real numbers, find the following values for the given function. The function is…

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Q: Evaluate: fx In xdx X ○ 25 (In x-²) 5 25 (In x-1) 5 + C O 25 (In x+²) 5 + C O None of these + C

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Q: The resistance R of a copper wire at temperature T = 30°C is R = 152. Estimate the resistance at T =…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the GS for y""+y"+y' + y = 1−x + e* - COS X

A: Given differential equation y'''+y''+y'+y=1-x+ex-cosx

Q: Evaluate the following integrals using substitution(s) 1. √ 2x(x² + 1) ²³ dx 2. [4e³x dx 3. [(1 +…

A: To evaluate : ∫2xx2+123dx ; ∫4e5x ; ∫1+cosx2dx We have to evaluate the above mentioned integrals…

Q: Consider the parabola given by the equation: f(x) = - 4x² - 6x + 7 Find the following for this…

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Q: y = sec² x, y = 8 cos x || 5|3 DEIM 17373 ≤ x ≤ 3

A: Graph:-

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A: Given, M(x)=-.015x2+1.43x-7.6

Q: Find Distance and Equations in R³ Find the distance in exact form between the point P(-4, — 2, 1)…

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Q: If x² + y² + z² = 9, dz dt = dx Š dt dy dt = 4, and = 3, find dz dt when (x, y, z) = (2, 2, 1).

A: x2+y2+z2=9 dxdt=4 and dydt=3 (x,y,z)=(2,2,1)   Differentiate the given function with respect to t:…

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Q: Find and classify (as a relative maximum, etc) all critical points of j(x, y) = 2x³ + 3xy + 2y³.

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Q: a) y = cos 2x on [0,1] b) x= on [1,10]

A: 6) a) y=cos(2x) on [0,π] the length of the curve is given by  L=∫ab(1+f'(x)2) dx here f(x)=cos(2x)…

Q: The graph below is the function f(x) -5 -4 -3 -2 -1 Find lim x 27 Find lim 5 4 3 2 1 x → 2 + -5 1…

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Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in…

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

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Q: Differentiate y = ex+2 +9.

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Q: A right circular cone has a radius of 5x+4 and a height of 3 units less. Express the volume of the…

A: A right circular cone has a radius of 5x+4 and a height of 3 units less. Express the volume of the…

Q: Find the absolute minimum of f(x, y) = x² − 7x + y² on the triangular region R that has vertices (0,…

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Q: Find an equation of the level curve of the function z(x, y) = ey (x² + y2) that passes through the…

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Q: Find the derivative of the following function:  y= tan-1(x) / x^4  and  log2 (x^2 + x - 1)

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A: Given vector:- rt=2ti+etj+e-tk

Q: 2. An equation like sin2 ? + cos2 ? = 1 is an identity because it is true for all values of θ. If…

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Q: The position of a free-falling object is given by s(t) = -4.9t² + vot + so where s(t) is measured in…

A: Note : As per our Guidelines , we can solve first three subparts .Please repost remaining subparts .

Q: A $360,000 building depreciates over time. The value y of the building after x months of use is…

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