For what values of "c" is the quadratic form q(x, y) = 3x2 — (5 +...

For what values of "c" is the quadratic form q(x, y) = 3x2 — (5 + c)xy + 2cy2 a) positive definite, b) positive semi-definite, c) indefinite?

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Rahul Sunny answered 2 years ago

5. Equations of the form y’ = P(x)y^2 + Q(x)y + R(x) are called Riccati equations....

5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) are called Riccati equations. i) If we know a solution y = φ(x) of this equation, then any other solution can be written in the form y(x) = φ(x)+ 1/v(x), where v(x) is an unknown function which satisfies a certain linear equation. Using the fact that φ and y both solve the above Riccati equation, find the differential equation that v satisfies. ii) Consider the equation 3y’ +...

5. Equations of the form y’ = P(x)y^2 + Q(x)y + R(x) are called Riccati equations....

5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) are called Riccati equations. i) If we know a solution y = φ(x) of this equation, then any other solution can be written in the form y(x) = φ(x)+ 1/v(x), where v(x) is an unknown function which satisfies a certain linear equation. Using the fact that φ and y both solve the above Riccati equation, find the differential equation that v satisfies. ii) Consider the equation 3y’ +...

f(x) = -3x2+16x-5 e) Find (in y=mx+b form) the equation of the line that contains the...

f(x) = -3x2+16x-5 e) Find (in y=mx+b form) the equation of the line that contains the vertex and the largest of the x-axis intercepts. If there are decimals round to the tenths place. f) Find the length of the line segment that is between the vertex and the largest of the x-axis intercepts.

5. Given the function y = q(x) = (x^2)/(x-1) a. What is the domain of q(x)?...

5. Given the function y = q(x) = (x^2)/(x-1) a. What is the domain of q(x)? b. What are the vertical asymptotes? c. What are the horizontal asymptotes? d. Where is q(x) increasing/decreasing (draw a line and specify by intervals – be sure to include points where q isn’t defined)? e. Where is q(x) concave up/down ((draw a line and specify by intervals – be sure to include points where q isn’t defined)? f. Find rel max/min. g. Find inflection...

For which values of x (if any) is f(x) = 2x3 + 3x2 – 12x –...

For which values of x (if any) is f(x) = 2x3 + 3x2 – 12x – 7 Increasing at an increasing rate?

Prove that P1, P2 ⊢ C P1: (∀x)(∃y)(P(x) ⇒ (Q(y) ∧ T(x, y)∧ ∼ S(x, y)))...

Prove that P1, P2 ⊢ C P1: (∀x)(∃y)(P(x) ⇒ (Q(y) ∧ T(x, y)∧ ∼ S(x, y))) P2: (∃x)(∀y)(P(x) ∧ ((Q(y) ∧ R(x, y)) ⇒ S(x, y))) C: ∼ (∀x)(∀y)((P(x) ⇒∼ T(x, y)) ∨ (Q(y) ⇒ R(x, y)))

Given the curve C in parametric form : C : x = 2cos t , y...

Given the curve C in parametric form : C : x = 2cos t , y = 2sin t , z = 2t ; 0≤ t ≤ 2pi a) the velocity v(t) b) the speed ds/dt c) the acceleration a(t) d) the unit tangent vector T(t) e) The curvature k and the normal vector N(t) f) the binormal vector B(t) g) The tangential and normal components of accelertation

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square). b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square). b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the...

Sketch the level curves f(x, y) = c and the level surfaces f(x, y, z) = c of the functions for the indicated values of c.

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For what values of "c" is the quadratic form q(x, y) = 3x2 — (5 +...

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5. Equations of the form y’ = P(x)y^2 + Q(x)y + R(x) are called Riccati equations....

5. Equations of the form y’ = P(x)y^2 + Q(x)y + R(x) are called Riccati equations....

f(x) = -3x2+16x-5 e) Find (in y=mx+b form) the equation of the line that contains the...

5. Given the function y = q(x) = (x^2)/(x-1) a. What is the domain of q(x)?...

For which values of x (if any) is f(x) = 2x3 + 3x2 – 12x –...

Prove that P1, P2 ⊢ C P1: (∀x)(∃y)(P(x) ⇒ (Q(y) ∧ T(x, y)∧ ∼ S(x, y)))...

Given the curve C in parametric form : C : x = 2cos t , y...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Sketch the level curves f(x, y) = c and the level surfaces f(x, y, z) = c of the functions for the indicated values of c.