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?

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

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.

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...

Let x,y ∈ R satisfy x < y. Prove that there exists a q ∈ Q...

Let x,y ∈ R satisfy x < y. Prove that there exists a q ∈ Q such that x < q < y. Strategy for solving the problem Show that there exists an n ∈ N+ such that 0 < 1/n < y - x. Letting A = {k : Z | k < ny}, where Z denotes the set of all integers, show that A is a non-empty subset of R with an upper bound in R. (Hint: Use...

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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 –...

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

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.

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...

Let x,y ∈ R satisfy x < y. Prove that there exists a q ∈ Q...