Give the substitution that converts the given nonlinear equation into a linear equation then find the general solution y'-y=-y³

Q: 1. Determine the equations of the tangent and normal lines at P(1,1) given x³y - 2xy² + x² - 3y + 3…

A: To determine the equations of tangent and normal to the given curve.

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Question 6 Determine the derivative of - sec z cosz-sin r sec" tan z sec² z 1-sin z sec² z O cos²x -…

A: Take y= Sin(x)/Sec(x)

Q: How long is the radius of the circle with center at (-4,5) and tangent to the y- axis?

A: Given query is to find the radius of the circle.

Q: The third derivative of the second derivative of y = f(x) is also O y(4) Oy (3) O f(5) (x) O D²y

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Q: Find the constant of integration for the DE dQ 2 + dr -Q=4; Q(2) = 100. 10+ 2r Select one: O a. 1306…

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Q: b) Is the integral f x(In x) P sina de convergent? Explain why! a

A: To determine  whether the integral ∫01sin xx dx is convergent. To explain why.

Q: Find the Laplace transform of the function. f(t) = 8e²cos3t

A: The given function ft=8e2tcos3t We have to find the Laplace transform for ft.

Q: Find sec 0 if tan 0 sec A Get Help: Video - 15 8 and cos > 0. Answer exactly. eBook Preview TIP…

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Q: Step 3 Now write the derivative in terms of x by recalling that u = -3x + 7 and v = x + 7. du 1 +=…

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Q: Hello,  Could I please get help with this discrete maths question.  I'VE ATTACHED A PICTURE OF THE…

A: Your solution is correct.

Q: What else do you observe? Concept Check: Evaluate the following integrals: 4. f 55 5sin2x *cos2x dx…

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Q: 1. Find the Critical values. for f(x) = x² + 4x³+4x²

A: GIVEN :fx=x4+4x3+4x2

Q: Draw - 7T in standard position. Answer in radians, the □ is already given. 4 -5 -4 -3 -2 -1 Clear…

A: We need to plot the angle :

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Let f be a differentiable function. A line is tangent to both of the curves y= √1+x2 and y = f(x)…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Combine into a single logarithm log3 - 4 log; y + 2 logą z − 2 O 10g3 O log3 2yª O 10%3 gyt 2½ O…

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Q: Solve the inequality. State the solution in interval notation: 6x4 + 12x³ < 48x²

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Q: Question 2 Let f(x, y) = 5e¹* sin(3y) af д х af dy =

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Q: h) R = 3qe 9

A: Given data:- The given expression is, R = 3qe-q

Q: y = 5x³

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Q: Find the general solution of the given differential equation. 6  dy dx + 42y = 7 1.Give the largest…

A: Solution is given below:

Q: dy 9. Given the curve xy - y³ = 7, find dx y [A] xyz [B] 3y x-y² y [C] -²/3 [D]x-3y [E] y x-3y²

A: On solving this we will get

Q: 0.12 200e

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Q: Concept check: Evaluate the following integrals and use the appropriate transformations when needed.…

A: Need to find out the integration.

Q: Find three positive numbers whose product is 86 such that the sum of their squares is as small as…

A: Let the three numbers be x, y and z. x + y + z = 86 -----(1) ⇒ z = 86 - x - y ------(2) Product, P =…

Q: g(x) = 25x² (a) (¹) (b) (c) (d) 1 g(a) g(√a) ✓g(a) Additional Materials

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Q: Find two positive numbers satisfying the given requirements. The product is 1200 and the sum of the…

A: Let the number be x and y Given: xy = 1200 To find x, y for which x + 3y is minimum

Q: Solve x + (3x + 1)y=e-3x dx Select one: O a. y = xe-3x + ce-3x O b. y = e-3x + cx-¹e-3x O c. y=e3x +…

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Q: Problem 1 Given a first-order differential equation: √1 + x² dy - ydx = 0 a) What is the best…

A: We have to find the general solution and the particular solution of the given first order…

Q: Evaluate the following integral using trigonometric substitution. 9|N 9 2 0 dx 2 √√81-x² dx 2 √81-x²…

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Q: 4. Find an equation of the tangent plane to the surface xy + yz+zx = 3 at the point (1,1,1).

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Q: Evaluate the following integral using integration by parts. fxsin 6x dx

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Q: r(t) = (0,8 cos³ 10t, 8 sin³10t), ≤ t ≤ 4

A: I am attaching image so that you understand each and every step.

Q: What else do you observe? Concept Check: Evaluate the following integrals: fe3xe 1. -5x dx

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Q: Find the solutions of the following IVPS or DE. a. y" — 4y' + 4y = e²x, b. y" - 2y = e2²x +3, y(0) =…

A: See the details solution in below

Q: Compute the surface area of revolution of y S I 4x + 3 about the x-axis over the interval [0, 5].

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  the given interval…

Q: Find the directional derivative of f(x, y) = √xy at P(7, 7) in the direction from P to Q(3, 4). Duf…

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Q: Given a first-order differential equation: /1 + x² dy-ydx = 0 a) What is the best solution method in…

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Q: dv 22² = 3/ dt v-1 32 a) Write the given first-order LDE in standard form. b) Solve for the general…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: 100 56. Σ (3k + 4) k=1

A: Note: Since the student has mentioned to solve only question no. 56, so we are solving accordingly…

Q: Find the derivative of the function: O y = a + (In²a + ln x + 1) O y = 2+1 ¹+¹(x ln² x + ln x + 1)…

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Q: Let f(x) = √22 – 3x and g(x) = -5x - 9. • You must combine all like terms before you submit your…

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Q: Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region…

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Q: Evaluate a multi-variable function Let f(x, y) = √√150 - 2x² – 4y², and evaluate f(1, 0). Please…

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Q: 1. (a) (b) Find and sketch the domain of the function f(x, y) = = Show that x²y² lim (x,y) →(0,0)…

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Q: Find the derivative of: Ř(t) = (sin² (3t + 1), ln(t² − 1), ²+1 –

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Q: Carl

A: Given - First 100 natural or counting numbers,  I.e.   n=. 1,2,3,4,5.......100. Required- Sum of…

Q: Solve cosx dx + (sinx)y=1 Select one: O ay sinx + ccosx O b. y = 2sinx + 2cosx + c O c. y = sinx –…

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