Find the eigenvalues of the matrix -40 -18 2 -8 -18 -14 -8 -18 -14, Enter the eigenvalues as a list separated by commas. If an eigenvalue is repeated, be sure to enter it as many times as its multiplicity.

Q: ind the curvature of the space curve. r(t)=-5i + (t+8)j + (In(cost)+1)

A: r(t)=-5i + (t+8)j + (In(cost)+1)kTo find:Curvature of the sapce curve

Q: Use logarithmic properties to find the exact value of log17 (175).

A:

Q: Given the function f(x) = 7x+3 - 9e Determine the equation of the tangent line at the point (0, -6).

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Q: Evaluate the following limit. (7x² - y²) lim (x,y)→(6, -6)

A: Let,

Q: Compute the following values for the given function. f(x, y) = 3xye(x² + y²) f(0, 0) = f(0, 1) =…

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Q: 3. A particle moves according to a law of motion s = where t is measured in seconds and s is…

A: Given:

Q: Let L be the line segment between (1, 2) and (4, -4). Find the area of the surface generated when L…

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Q: Determine the derivative of the following function with respect to a: 75 +¹rsin (r) 4,

A: f(x)=π5+π4xsin⁡(x)

Q: Nû 4 - x X X dx

A:

Q: 4. A suspension bridge with weight uniformly distributed along its length has twin towers that…

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Q: Set up the definite integral required to find the area of the region between the graph of y = x² -…

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Q: Solve the following differential equations using Exact method ху (2+ye Jdx + (x-2y) dy =0

A: we need to find out the solution of the exact differential equation.

Q: Find the length of the parabolic segment r= 14 1 + cos 0 The length is (Type an exact answer, using…

A:

Q: Find an upper bound error in estimating 3 [cos (3x) dx using the trapezoidal and Simpson's rule with…

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Q: 2. Determine d (sin-¹(x²-1)). dx Simplify your answer as much as possible.

A: Consider the function

Q: If f(x)= = 3x5 – 5x4 – 3x³ x4 " find f'(x).

A: The given function

Q: Suppose z = x² sin y, a = 48² t², y= 8st. A. Use the chain rule to find and all x, y, s and t in…

A: z=x2-t2 ,y=8st

Q: The compound interest formula is given by nt A = P(1 + 2)² where A is the accumulated amount, after…

A:

Q: (c) h(y) = 754 h'(y) = * ( = 7 (5(~²))* = 7 @y= √√x + √x + √ (d) dy dx

A: The given function,

Q: Find the equation for the tangent plane to the surface 4x2+10y2-z=0 at the point (2,1,26)

A: 1. Calculate the gradient of the surface at the given point (2, 1, 26). The gradient is a vector…

Q: 1. Change the equation x² + y² + 6x - 16 = 0 to standard form and determine the coordinates of the…

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Q: The definite integral: Use geometry to find (2+√9-x²)dx. a.

A:

Q: Find the first partial derivatives of f(x, y) = 9x³y° + 6x³y² +2. af ax ||

A: Given, .Formula of partial derivatives:

Q: Sketch the graph y = sin(x) along with its tangent line through the point (0,0)

A: The given equation of function

Q: In(19/t+1) 4/t Minimum Level of Stabilization: 2.73125 Maximum Level of Stabilization: 3.740625…

A: Minimum level of stabilization: 2.73125Maximum level of stabilization: 3.740625

Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 15 m/s, its height…

A:

Q: 6 Use the following methods to estimate fdx: X 2 a. Left endpoint approximation L 3 b. Trapezoidal…

A:

Q: (i) (k) dx (tan x) dx (secx) = = (j) (cscx) = dx (1) :(cotx) = =

A: As per your request, we answer only parts (j) , (k) and (l).find using derivative rules

Q: Consider the following function. x ≤ 1 (3x + 2, 16-x², x > 1 (a) Find the critical numbers of f.…

A: The given function

Q: Find the derivative of the function at P0 in the direction of u. f(x,y)=4x2+3y, P0(7,10), u=3i-4j

A: f(x,y)=4x2+3y, P0(7,10), u=3i-4j

Q: 4. Find the exact length of the curve. x=e' -t, y=4e¹¹2, 0≤t≤2

A:

Q: 7x 1+2x 2+1 x_3+8 x_4+9x_5 = 69 9x 2+3 x 3+4x_4+4 x 5 = 54 4x 1 + 6 x 2+5 x_4+4 x 5 = 40 2x 1 + 10 x…

A: We solve the following system of linear equations using the Gauss-Jordan Elimination Method:

Q: Find dy clx In (sin(8x3)) a) y=(√√x2-1) In (sin( b) y = 1+ sin ² (3x)+sin 4 (3x) + sin 6 (3x)+.... +…

A: Since, you have posted multiple questions.As per guidelines we are supposed to answer only first…

Q: Find the derivative of the function. y' = y = √√√1-x² - x cos-¹(x)

A: we need to find out the derivative of the given function."Note that as per the rules, we are…

Q: Find the derivative of the function. f(t)=√3+ tan(t)

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Q: Suppose that a colony of Jeevesium beetles grows exponentially with doubling time 7 years. How many…

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Q: 4. Find a formula for the nth derivative f(n)(x) of f(x) = ln(1+3x). Show some work computing the…

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Q: 10. A 12m ladder is propped up against a wall. If the bottom of the ladder slides away from the wall…

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Q: ind  dy/dx  by implicit differentiation. x4(x + y) = y2(5x − y)

A: The given equation is

Q: Find the length of the curve x = 6y from y = -5 to y = 5. Write the exact answer.

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Q: Find the length and direction of u x v. u=4i+2j+8k, v=-i-2j-2k

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: If f(x) = 4√√x(x³ - 8√√x+6), Find f'(2). find f'(x).

A: If .To find .

Q: th Compute the first four partial sums S₁, ..., S4 for the series having n follows. an = (−1)¹6 S₁…

A: By finding the first four terms, we can then find the first four partial

Q: Given: x=t², y=t-8, -4≤t≤4 a) Sketch the curve by using the parametric equations to plot points.…

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Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (5, 5) in the direction = 3/4…

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Q: The velocity of a particle moving along a line is a function of time given by 79 t² + 12t + 27 v(t)…

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Q: Solve the differential equation. du dt = (5t^4)/(ut^2+u^4t^2)

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Q: A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must…

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Q: Let f be a differentiable function. We are given the following values of ƒ and x |ƒ(x)|ƒ'(x) 4 16 36…

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