Use an appropriate substitution to solve the equation Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = yl-n transforms the Bernoulli equation into the linear equation and find the solution that satisfies y(1) = -6. y(x) = dy dx du dx + P(x)y = Q(x)y". + (1 − n)P(x)u = (1 − n)Q(x). xy + y = 7xy²,

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A: we need to find the number of years to take the world population double.

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Q: Find the radius and center of the sphere. [Hin 2x² + 2y² + 2z² +4x-16z = - 18

A: The given equation is  2x2+2y2+2z2+4x-16z=-18  Find the radius and center.

Q: Evaluate each of the following integrals. 43. I dz I¹ + az 1 Ans. - In a z z+a + C.

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Q: 9. Let f(x) = cos 2x. Calculate f(50) (x), the 50th derivative of f(x).

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A: Note:- According to guideline we can do 1 question so i am solving first question all sub parts.

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. = cos(¹x). y…

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Q: 2. Let m and b be rea If fis both continuo

A: Topic:- calculus

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Q: slve the following I.V.P do +=y=y² Y= da B.C = (P.G.) 56). 1 3

A: Given differential equation:- dydx+12y=y3

Q: a. b. 1. C. d. e. f. g. h. i. j. (2y³ +42) dx = (6-2xy²) dy y² = ex s = [C(x - C₂)]³ 9y+2 y -to (sec…

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Q: If xy + 5y = 2 then find (-4, 2) in simplest form. d'y dx² at the point

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A: maximum value=28 minimum value=-4

Q: If tant 7. what is tan (t - π)? Enter the exact answer. tan (t - π) = =

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Q: II. For each of the following ellipses, find the center, principal axis, vertices, co- vertices,…

A: Concept: In mathematics, an ellipse is the location of points in a plane so that their separation…

Q: 4. dy 2x = (3y + x). dx

A: As per the company rule, we can answer only the first question and rest can be reposted.

Q: Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y),…

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Q: Find the volume generated by rotating the given region about the specified line. ℛ1 about A B

A: Let's find volume when rotated region R1 about line AB.

Q: The cartesian coordinates of the point P is: ← A 0 2 1 32 R P (1, 0, 3) AC (1, 2, 3) BC (1, 2, 0) Co

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Q: Find a  variation constant and an equation of variation for the given situation.   3. y varies…

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Q: . y = sec(x)√1+cot² x csc³(x)

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Q: d) e) U₁U4 = Round your answer to 3 decimal places. V1 V3 = Round your answer to 3 decimal places.

A: Given vectors  v1=8−9v2=75v3=4−6v4=90

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Q: Evaluate the integral by interpreting it in terms of areas. L₁ (5+ √1-x²) dx

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Q: Solve each of the following by forming exact differential (2y + 2xy2-xªy)dx +(x³ + 2x2y-x)dy-0

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Q: dy Find when dx x(t) = 3te, y(t) = 4tet. 1. 2. 3. 4. dy dx dy dx dy dx dy dx 3e¹(1+t) 4 + et 3e (1…

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Q: 1. g(x)=3 tan¹ 3x 2. y=xsin ¹2x+cot ¹ √ 3. f(x) = sin ¹

A: Let's find derivative of given function.

Q: lim x →0 64-1 X

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Q: Find the radius of curvature of y = In(x + 1) at point (7, In(8)).

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Q: 1. Determine the differential equation by elliminating the arbitrary constants y = A·e + Bxe*+ Ce*

A: Differentiate given equation 3 times and solve equations to get differential equation

Q: 4. y = (arc csc 2x)

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Q: For the function f(z)=-2sin (-). determine its amplitude and period, and then graph it for two…

A: Given a the trigonometric equation of the sine wave, y=Asin(Bx+C)+D Amplitude is |A| Period is 2π|B|

Q: dy Solve the following implicit partial derivative dx and select the correct answer:…

A: sol is given below..

Q: Find the gradient of f(x,y,z)=xyz^2.     ∇f=_______ i+_______ j+ ________  k

A: We can solve as follows

Q: Find dy dt dy dt at x = - 1 if y= 4x² + 4 and dx dt _ 3.

A: A detailed solution is given below.

Q: V. Identify the value/s of x for which the corresponding function evaluation is true. Show complete…

A: Topic = Functions

Q: 1. x²-2x-24y+1=0 Standard Form Equation: a. Vertex: b. Focus: C. Length of LR: d. Directrix:

A: Topic = Parabola As per guidelines , At a time only one question with three sub-parts can be…

Q: Suppose f is a one-to-one differentiable function and its inverse f^-1 is also differentiable.  a).…

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Q: ft A ladder leans against a vertical wall. If the top of the ladder slides down at 2.5- elevation of…

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Q: Design a differential equation whose fundamental solutions are y₁ (t) = e-t/2 and y2(t) = e-2t.

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Q: The scalar projection of the vector onto the vector is: 6 10 3√5 10 7 1123 BC CC DC

A: See the details solution in below

Q: Factor the following expression completely given that one of the roots is -6: w³+1w² - 44w - 84 =

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