Question

2. Let Q1 = y(2), Q2 = y(3), where y = y(x) solves y' + 2xy = 2x^3 , y(0) = 1. Let Q = ln(3 + |Q1| + 2|Q2|). Then T = 5 sin^2 (100Q) satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T < 3. — (D) 3 ≤ T < 4. — (E) 4 ≤ T ≤ 5.

Answer #1

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Let Q1 be a constant so that Q1 = L(−3, 2), where z = L(x, y) is
the equation of the tangent plane to the surface z = ln(5x − 7y) at
the point (x0, y0) = (2, 1). Let Q = ln(3 + |Q1|). Then T = 5 sin2
(100Q)
satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T
< 3. — (D) 3 ≤ T < 4. —...

Let Q1, Q2, Q3 be constants so that (Q1, Q2) is the critical
point of the function f(x, y) = xy + y − x, and Q3 = 1 if f has a
local minimum at (Q1, Q2), Q3 = 2 if f has a local maximum at (Q1,
Q2), Q3 = 3 if f has a saddle point at (Q1, Q2), and Q3 = 4
otherwise. Let Q = ln(3 + |Q1| + 2|Q2| + 3|Q3|). Then T =...

Let Q1 be a constant so that Q1 = L(5, 17), where z = L(x, y) is
the equation of the tangent plane to the surface z = x 6 + (y − x)
4 at the point (x0, y0) = (3, 4). Let Q = ln(3 + |Q1|). Then T = 5
sin2 (100Q)
satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T
< 3. — (D) 3 ≤...

Let Q1 be a constant so that Q1 = L(20, 12), where z = L(x, y)
is the equation of the tangent plane to the surface z = ln(19x +
8y) at the point (x0, y0) = (7, 11). Let Q = ln(3 + |Q1|). Then T =
5 sin2 (100Q)
satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T
< 3. — (D) 3 ≤ T < 4. —...

Let Q1, Q2, Q3 be constants so that (Q1, Q2) is the critical
point of the function f(x, y) = xy − 5x − 5y + 25, and Q3 = 1 if f
has a local minimum at (Q1, Q2), Q3 = 2 if f has a local maximum at
(Q1, Q2), Q3 = 3 if f has a saddle point at (Q1, Q2), and Q3 = 4
otherwise. Let Q = ln(3 + |Q1| + 2|Q2| + 3|Q3|). Then...

let Q1= y(2) and Q2= y(3) where y=y(x) solves...
(dy/dx) + (2/x)y
=5x^2
y(1)=2

Let Q1, Q2, Q3, Q4 be constants so that y =Q1+Q2x+Q3x^2+Q4x^3
satisfies that y(1)=1 and (1-x^2)y"-2xy'+12y=0.

Let Q1=y(1.5), Q2=y(2), where y=y(x) solves y'+ycotx=y^3 sin^3x
y( π/2)=1
Please show all steps!
Thank you!

) Check that each of the following functions solves the
corresponding differential equation, by computing both the
left-hand side and right-hand side of the differential
equation.
(a) y = cos2 (x) solves dy/dx = −2 sin(x) √y
(b) y = 4x + 1/x solves x dy dx + 2/x = y
(c) y = e x 2+3 solves dy/dx = 2xy
(d) y = ln(1 + x 2 ) solves e y dy dx = 2x

Let F ( x , y ) = 〈 e^x + y^2 − 3 , − e ^(− y) + 2 x y + 4 y 〉.
a) Determine if F ( x , y ) is a conservative vector field and, if
so, find a potential function for it. b) Calculate ∫ C F ⋅ d r
where C is the curve parameterized by r ( t ) = 〈 2 t , 4 t + sin
π...

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