For the following exercises, use the second derivative test to identify any critical points and determine whether each critical point is a maximum, minimum, saddle point, or none of these. 335. _ƒ(x, y) = x² + 10xy + y²

Q: Find the general solution of (d²s)/(dt²) + 2(ds/dt) + 5s = 0. OA.y = C₁e(t) cos2t + C2 e(t) sin3t…

A: Let's solve given diffrential equation.

Q: Three forces with magnitudes of 5 pounds, 8 pounds, and 120 pounds and direction angles of 90°,…

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Q: -3 (x² - y²)²] Evaluate: ₁²² x+y du dt

A: Given

Q: Evaluate: xy² dx dy [√ 0

A: We have to find value of given definite double integration.

Q: A stone, projected vertically upward with initial velocity 112ft/sec, moves according to…

A: Topic = Algebra The maximum height reached by the stone is 196 ft.

Q: Evaluate: ²₁²²-²² du (x²-y²)²] S du dt x+y

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Q: Sy² sin Sy dy 1 A) ----² cos Sv + y sin y sin Sy + 1 256 32- 1 1 B) ² cos By-y sin Sy-256 9-11-² sin…

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Q: 2 (x² - y²) ² Evaluate: ³₁² L 21 x+y du dt

A: We have to find value of given double integration.

Q: Evaluate the integral: f/2² sin (-) dt du ,2

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Q: Find the area of the region bounded by the curves 1 y = (x+6)²¹ Y = 4 and the x-axis using vertical…

A: Given

Q: Evaluate the following * [csc² cot (5x+6)/2 + C cot(5x+6)/ 5+ C - cot(5x+6)/ 5+ C cot(5x-6)/ 5+ C…

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Q: 3 Evaluate: ³₂²₁¹ [2³(x + y)³] dz dy dx

A: This is a problem related to triple integration. Based on the general formula and concept we will…

Q: Evaluate: ₁₂₁(4x²y — z³) dz dy dx J1

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Q: valuate: xy² dx dy

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Q: Find the area of the region pictured below that is bounded by the functions f(x) = x² - 7x + 12 and…

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Q: mydx = nxdy

A: answer is in next step . please give a like !!!

Q: ¹₂1 + 2y dy dx x2

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Q: 2 3 Evaluate: y cos(z5) dx dy dz 0

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Q: a. Arc length of the curve y = 4- (x-2)² 4 bordering the region R

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Q: Use the table of integrals to evaluate the integral. 2 √2²47x²³ √4x²-x+ d² dx

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Q: 2x-1 Q7. Find the convergence interval and radius of the series : 2 (-1)" . Σ(-) 2n-1 n=1

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Q: Does the Rolle's Theorem applies for f(z) – ln(2 – z²) over the interval [−1, 1]? O Cannot be…

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: 5x 2 Evaluate: f fx fdz dy dx 2

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Q: Evaluate: ff xy² dx dy

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Q: Derivative of arctan(ln(n))

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Q: The derivative of y with respect to given a = 1 is Onone of the choices O y = yx³-1 O V = 0 = = 9 *…

A: I have stated the used formula in the solution

Q: Determine the intervals on which the function is concave up or down and find the points of…

A: topic- inflection points and concavity

Q: Evaluate: xy² dx dy

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Q: Determine the values of r for which the differential equation y + 2y = 0 has solutions of the form y…

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Q: Use the table of integrals to evaluate the integral. 2 5x³√4x² - x4 dx

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Q: True or False: Given a vector v, the vector -v will have an opposite magnitude. A True B False

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Q: Evaluate: du [(x²-y²)²1 ³₁ 1² du dt x+y

A: Given , ∫-13∫02x2-y22x+ydudt

Q: Fill in the blanks to determine which polar coordinate pairs name the same point. The questions are…

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Q: A) Match each equality with the letter corresponding to the property it illustrates. Responses may…

A: 1) Associative property of addition (8+2)+4=8+(2+4) 2) commutative property of addition…

Q: t sin (=) dt du

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Q: 3 Evaluate: £³₂ √²₁ ₁²[z³(x + y)³] dz dy dx

A: Given :∫-23∫-12∫01z3x+y3dzdydx

Q: 4 nd the area of the region bounded by 2x = y²+1 nd the y-axis using the horizontal strip.

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Q: 3x(xy - 2)dx + (x³ + 2y)dy = 0; f(1)=2 Find the positive root of y at x=2. Use 2 decimal places.

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Q: The function g is continuous on the closed interval [1, 4] with g(1) = 5 and g(4) = 8. Of the…

A: This question can be solved using the concept of Mean Value Theorem.

Q: Evaluate the integral: S/2 sin(4t - u) du dt

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Q: True or False? 4. Let f : R → R be a function defined by f(x) = x^2+1. If B = {2, 5}, then…

A: according to the company rule we can answer only the first question and rust can be reposted.

Q: solve the equation! - A (a) Y'(t) = -Y(t) + sin(t) + cos(t), Y(0) = 1; Y(t) = sin(t) + ce-t. b)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 6. What is the measure of the angle 0 between the vectors u : = (6, 2, 1) and 7 = (−4, 1, 2)?

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Q: integral: 2² sin (-) dt du Evaluate the integral:

A: use substitution method and integration of parts for solving the integral

Q: If lim f(x) = -∞, then which of the following is TRUE? I-0 O None of these. Ox= = 0 is a vertical…

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Q: •π * (sin³ x)√1 + cos x dx 2

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Q: A manufacturing company is responsible for designing a can for diced tomatoes which will have a…

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Q: Q9. If W = f(u)=u' + sinu+Inu, and a=ax+by, where a, and b are constants, show that aw aw b. ax

A: We have to prove the given statement.

Q: ๆ ³₁₂₁ (4x²y — z³) dz dy dx -2 J1

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Q: w = 4x + y² +2²³₁ x = ers²₁, y = 1 y = In(r+s).

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