Find the divergence of F(x, y, z)= x î+y³ ₂² 7 +xz³ k. O1+3y²z²+3xz O1+3y²z²+3xz² 01+3y²₂² O 1

Q: 1. Choose a solution to the differential equation y" - y = x²e² + 5.

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Q: 9 Given f(x): = =, find f'(x) using the limit definition of the derivative. x f'(x)=

A: The given function is fx=9x

Q: 6. Find the y" + y = sec³ x; y(0) = 1, y'(0) = 1. -√2 value (7) for a solution (x) to the initial…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: Find ▼ × (V × F) if F(x, y, z) = 10xyj + 5xyz k. ▼ × (▼ × F) : =

A: To find ∇×∇×F if Fx, y, z=10xy j+5xyz k.

Q: Given: f(t) = 3t4 + 6. Evaluate: F(3) Use 2 decimal places. 2.30

A: Here we have to apply laplace transform.

Q: Find the gradient of the function f(x, y) = sin(x + 2y) O cos(x + 2y) [2î+î] cos(x + 2y) [i+1] O…

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Q: Answer true or false. The function f(t) = (et) 10 is of exponential order. O True O False

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Q: Solve the DE: 2 dy 3 dx 3x² + y² xy

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Q: f(x) = 2x^3 − 3x^2 − 18x − 8 Rewrite f(x) using the Division Algorithm after having found one…

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Q: Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x)…

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Q: The weekly marginal cost of producing x pairs of tennis shoes is given by the following function,…

A: The weekly marginal cost of producing x pairs of tennis shoes is given by the following​ function,…

Q: Use an appropriate linear approximation to estimate (Round your answer to three decimal places.)…

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Q: Show that the differential equation x³y² + x(1+yº)y' = 0 is not exact, but becomes exact when…

A: To show that the differential equation x6y7+x1+y6 y'=0 is not exact, but becomes exact when…

Q: Which is the center and radius of the circle given by the equation, x² + y² - 6x 10y + 11 = 0?

A: The answer as follows:

Q: Consider the function f(x) = 3x² 10x + 10, 0≤x≤ 6. The absolute maximum of f(x) (on the given…

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Q: 16 x0.67.dx

A: Formula  ∫xndx=xn+1n+1+c

Q: ANSWERS Newton's law of cooling states that the temperature of an object changes at a rate…

A: We will find the required solution.

Q: 8 1 3√x 1² O 0.5 O 6.5 O 4.5 O 0.5 dx

A: Given a definite integral ∫181x3dx We have to choose one of the given option solving the given…

Q: 0 xsin2x x² + 3 -dx =?

A: Given: ∫0∞x sin2xx2+3dx

Q: ટા ભpl7+KZ+x) iળ પશ8 છas buwગારા વા મૂળ પગપા

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Q: Sketch the region D of integration, and then evaluate the integral by reversing the order of…

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Q: Find the Taylor series generated by f at x=a. f(x) = 5x , a = 7

A: We have to find Taylor series of f(x) =5x about x=7. Let us see first what is Taylor series…

Q: Determine the points of discontinuity for the following. 2x+5 f(x) = X-7x+6

A: F(x)= (2x+5)/(x^2-7x+6) Factorise the denominator F(x) = (2x+5)/(x-1)(x-6) Denominator can not be…

Q: If u = X + y+z a) 0 y 2+x ди + then the value of x x+y x b) 1 c) u d) None ax +y + ay +2 ди əz IS:

A: Question - 21 Given, u=xy+z+yz+x+zx+y To find, x∂u∂x+y∂u∂y+z∂u∂z Formulas used:…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Given, L-11s2+1s2+25

Q: For the function f(x) = 3x2 −x3 − 4 where −3 ≤ x ≤ 3, complete the following. 1. Find f′ and f′′.…

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Q: Solve: x"-x+ 5 y'=t y" - 4 y-2x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: What is the gradient of f(x, y, z) = x³z2 + y³z +125z - 1 at P(5,5,-1) ?

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Q: Find curl (62 i + 7x j + 2y k). curl (62 i + 7x j + 2y k) = (i )k )i + (i )j + ( i

A: Here we have to find the curl.

Q: 14. The solution of the differential equation: (D-2)³y = e2²x is k a) y = (₁ + c₂x)e²x + xe²x b) y =…

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Q: A solid right circular cone is made of brass. The mass of the cone is 5080 grams, to the nearest 10…

A: Formula to calculate :-Density=MassVolumeVolume of the cone=13πr2hwhere r=radius of the base of the…

Q: Determine the independent and dependent variables on the given differential equation: - (5²) -15…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: This question is related to definite integration, we will solve it using given information.

Q: Use the properties of the derivative to find[r(t) × u(t)] given the following vector-valued function…

A: As we know that; The Sum/Difference Rule: f±g'=f'±g' The Power Law: ddxxn=nxn-1 And a·f'=a·f', where…

Q: Obtain the particular solution of the equation: 2ydx = 3xdy; when x = -2 and y = 1 ° y = (2x (2x)=3/…

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Q: Find the area inside the oval limaçon r = 6 + sin 0.

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Q: Consider the points P(1,0,3) and Q(5, 2, -1), and the line 1: { x = -7 - 2t y=t z = 9+t

A: part :a

Q: Find a unit vector u in the direction opposite of v = (2,8,-3).

A: Solution ) v =  { 2 , 8 , -3 }   vector with same magnitude and opposite direction   = { -2 , -8 , 3…

Q: Use the triangles given on the right to evaluate the expression given below. If necessary, express…

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Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y+3y" - 3y - 2y = et,…

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Q: b) sin (2x) tan (5x) Find lim- (Can't use L'Hospital's Rule)

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Q: Which of the following is not a unit vector? 2 A. • (-3/35.0,-/) √5' √5 B. (cos 1, sin 1, 0) C. (1,…

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Q: Find the equation for ​(a) the tangent plane and ​(b) the normal line at the point P0(1/2,1,e) on…

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Q: (-9) Σ 5 0 = 1

A: The answer is given below:   Ration Test

Q: 1 Σ (3)"-wn + 4 n = 0 (n + 1)(n + 2).

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Q: potential

A: Please refer to the image below

Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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Q: 14. est 3 comment The critical numbers x = -7 and x = 5 are found from a continuous function f'(x).…

A: The critical numbers x=-7 and x=5 are found from a continuous function f'x f''(x)=1-x3x+6

Q: Solve for x at y=1; (1+y^2)dx + 2xy dy=0; y(-5)=2

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