12. Using reparation of variables, solve the differential equation, ey èy nincx) - dy cosa (x1 = 0 dx

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A: Given Function

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A: we have given

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Q: 2. Compute Jet ds for f(x, y) = √1+9xy and the curve C defined by the equation y = x³ for 0 ≤ x ≤ 2.

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Q: 1. Another way of writing 5-³ = A. log 1 5-3 125 13 is: B. log-35 = 1 125 C. logs 125 =-3 D. log5-3…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

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A: Initial amount= $55000The average rate of depreciation of the car is 7% per yearFinal amount =…

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Q: Using integration by parts, the integral f (sin-¹ x) dx becomes IT 12 +2 # ( So² da dz So T 12- Soda…

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A: The given equation is; z=5(x-1)2+3(y+3)2+6, (2,-1,23)Find the equation of the tangent plane to the…

Q: Given that f(x) dx = 3 and ſå f(x)dx = 4. 2 6 A) f f(x) dx = 2 B) f²2² 3 f(x) dx = 6 c) f f(x) dx =

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Q: Evaluate the indefinite integral as an infinite series. 6 £ ) n = 1 ex - 1 dx 5x 6e(5x") 1-1 ܐܐ…

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Q: Please show your answer to at least 4 decimal places. Determine the gradient of f(x, y) = e³²…

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Q: Use L'Hopital's rule to evaluate the following limit. Enter your work in the answer fields below. If…

A: The given limit is; Limx-0(x3+4x2)/(1-cos(pi x)).

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Q: Question 1 Two straight roads intersect at right angles. At a given instant, a car is 30 km from the…

A: We solve the given problem using the differentiation concept.

Q: Q2.41 z(t)= etle 0 0 t/5 e Z= 263 С1 C₂ is the general Solution linear syestem1 = Z₂. Figure out the…

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Q: Please show your answer to at least 4 decimal places. Determine the gradient of f(x, y) = e³ª…

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Q: square from each rectangular peice of cardboard and folding up the resting flaps, a box with no top…

A: Given a cardboard of size 30 inches by 30 inches, after cutting out squares of size x by x from each…

Q: 3 Evaluate the integral 1 = = = 3 dz -

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Q: If 5 11 f(x)da = 9 then the average value of ƒ(a) on the interval [5, 11] is 3/2. True O False

A: Given a statement  if then the average value of f(x) on the interval  is

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A: The given function is

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Q: Use Calculus to find the points on the curve where the tangent is horizontal or vertical. You have…

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Q: Compute In (7x) x4 S dx.

A: given integration

Q: Evaluate the definite integrals using the graph of f(z) below. (-) 6² 16 de b) √₂ ²1 (2) f(x) dx =…

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Q: Which statement is true about the infinite series It is absolutely convergent 1 In 2 + In 3 1 In 4…

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Q: For the given cost function C(x) = 48400 + 300x+x², =

A: C(x)=48400+300x+x2

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Q: Find the limit and determine if the function is continuous at the point being approached. lim tan…

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Q: Find the area between the regions y=sinx and y=1-sinx from [0,1/6] (2.5)+sqrt(3) O (π/6)+sqrt(3) - 2…

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Q: If cosa = 0.514 and sin ß= 0.801 with both angles' terminal rays in Quadrant-I, find the values of…

A: Given data

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Q: Consider the function f(x) = 2 + 3 ४।०७ +5e.

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Q: (a) Use differentiation to find a power series representation for 1 (3 + x)²· Σ((-1) "3" (n+1)x²¹…

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Q: Compute In (5x) [15 x (ln(5x))² 2 + C ○ 5(ln(5x))² 2 + C O 5(ln(5x))² + C O (ln(5x))² 10 + C O…

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Q: webassign.net Graph the function showing all relative extreme points and inflection points. f(x) =…

A: The given function

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A: There are more than one question so i will solve the first question. If you want answers of other…

Q: 14 Find the point (s) on the ellipse 4x² + y² = 4 that are farthest from (1,0). (Show your work)

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Q: Find the sum of the series. 00 n=0 e-(5n)2 3(n+1)! 57 37n! X

A: The given series .The aim is to find the sum of the series.

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Q: Compute √ 4x2 + 118 dx. (4x²-4x+10)8

A: The given integral is; (4x-2) /(4x2

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = xzi+yzj+3z²k across the boundary of the…

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