4. Find the equation/s of the normal line of slope 2 to the ellipse x² + 2y² = 3. 5. At what point is the tangent line to the curve y = x³ +5: a) parallel to the line

Q: 12. A thin 4 cm wire represented by 1 < x < 5 has density function p(x)=19/cm. Find the mass of the…

A:

Q: • show that (x, y, z) = PDE : 2²4 ахг 824 дуг + 2 x² + y² + z² = 0 8²4 dz² satisfies the

A: This question can be solved using the concept of partial differentiation.

Q: 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is…

A: Given that, A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator…

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A:

Q: Evaluate the double integral that will find the volume of a solid inside the paraboloid z = 1 - y² -…

A: Given function z=1-y²/4 -x² And xy plane  Volume V=∬zdydxV=∬1-14y2-x2dydxGIven z=1-1/4y2-x2 and…

Q: Find the slope of the tangent to the curve y = 3e^(2x) at (0,3)  a. 3  b. 2  c. 6  d. 12

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Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(9y) dy =…

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Q: y=u² +2u u=v² + 2v v = x² + 2x

A:

Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х ucx, c) - че 2 (зу-2х)12 ans3-…

A: To find the general solution of the given PDE .

Q: Consider the parametric curve: x = ln (8t) y = 5t³ Which integral gives the arc length of the curve…

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Q: 6) The graph of g'(t) on the interval [0, 10] is shown below. If g(0) = 3, find g(10). g'(t) 4 0 t

A: Let's find value of g(10).

Q: Sketch the graph of an example of a function that satisfies all of the given conditions limx)=0 lm…

A: TO FIND: Correct Graph of the function

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 3…

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Q: / If y" + 2y' F5y = e-Sint, y(0) = 0, y' (0) = 1

A: We solve the given differential equation using the higher order LDE techniques.

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

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Q: Find the solution of the given initial value problem. 8 y' - 7 y = cos t t-8 Y(T) = 0, t> 0 t y(t) =

A:

Q: àtics II, e the caraid Q3) By using the polar find region enclosed by y = x² and y = 1 Find the

A: Let's find region enclosed by curve and given line.

Q: Solve the given differential equation. All solutions should be found. dy x³-8y dx x NOTE: Use c for…

A: The given first-order differential equation is: dydx=x3-8yx⇒dydx=x2-8xy⇒dydx+8xy=x2...(1)

Q: 2 S Sec'x In cotx) dx (

A: We will solve the problem.

Q: Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable…

A:

Q: Consider the following quadratic function. g(x)=3x² - 6x-4 (a) Write the equation in the form g(x) =…

A: This question can be solved using the concept of general equation of parabola.

Q: swers: i i Mi 0 0 O

A:

Q: 2. Solve each of the following integrals using integration by part: a) [3x² In 2x dx b) 5x sin 3x dx

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Q: 9) y = вод по- 10) У th 4x 1+₂x exbx

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: IV. Evaluate: lim (x² + €¯²)(x-¹ csc csc z) z→0+

A: Given :limx→0+x2+e-xx-1cscx

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 4…

A: Given problem:- The radius r and height h of a cylinder are changing with time. At the instant in…

Q: و و ۹۷۶) (0) لا او A 2 1 - X Jx (x+2 - 4

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

Q: Let F(x,y)=ln(x² + y²), then answer the following (4) Find the boundary of the function's domain.…

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Q: Find the volume of the region bounded above by the sphere x² + y² + z² = 2 and below by the parabo-…

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Q: Q6. Let W = f(r,0), r = 0 = tan"'(y/x), find aw Ох > and ди ду in terms of r and 0.

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Q: Find the solution of the given initial value problem. ty' +4y=t²-t+7, y(1) = 4, t>0 y =

A:

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

A: Solution: The objective is to find the derivative of the given function

Q: 3 4. Find the length of the curve y = 7(6+x) 2 from x = 189 to x = 875. Submission status

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Q: For the curve x+y-y=1 complete the following parts. a. Find equations of all lines tangent to the…

A: This question is related to tangent to the curve, we will solve it using given information.

Q: Find the area of the region enclosed by the curves y = x³ and y = 4x. 24 8 16

A:

Q: Find the solution of the given initial value problem. y = ²7y= y' cos t t-7 Y(T) = 0, t> 0 y(t) =

A:

Q: Evaluate the double integral: 2 So de dy. Sola 0 Jy¹/3 Y x7 +1 (Hint: Change the order of…

A: Application of integration

Q: Q3: A) Find the limits below x² + sin²y 1) lim (x,y) (0,0) 2x² + y² 2) lim (x, y)-(1,1) x² - 2xy +…

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Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

Q: A- L [ Sin2t + cos2+] ² 2 B 32 3-2 [37-² + cost's *] 3 2

A:

Q: 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is…

A: Given problem:- 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a…

Q: When solving ff(u)du = t - e³u f(u)du you obtain 1 A) f(t) 1-e³t t B) f(t) 1+e³t t C) f(t) 1-e³t 1…

A:

Q: 4. Evaluate the double integral: L Lates y¹/3 x² 27 +1 (Hint: Change the order of integration to dy…

A:

Q: ∞ ∞ dx 2 x² +9

A: Given :∫-∞∞dxx2+9

Q: 7 Find the general Solution of the following PDES. -X • 3U XA2 Uy so > u(x,0) = 4 ex (3y-2x)/2 ans -…

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Q: 5. Use Cartesian coordinates to evaluate [[[ 1² av where D is the tetrahedron in the first octant…

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Q: 2. Find the area bounded by the two curves y=x²-6x²+ 8x and y = x² - 4x.

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Q: Given a second order differential equation dx 3t 2x = e³t dt where t = 0, x = -5. Using Laplace…

A:

Q: Find the area of the region enclosed by the curves y =

A: answer is in next  step

Q: Find the surface area of the composite figure. 14 ft 9 ft 9 ft 18 ft 10 ft SA 10 ft 10 ft 10 ft 14…

A: Concept: Area of the triangle=12base×heightArea of the square= side2Area of the rectangle=length…