If F(s)= 1 & G(s)= s+1 1 → Calculate the convolution ƒ (2) * g(2)=? s -1

Q: - (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with…

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Q: Solve the initial value problem for an arbitrary f(t) function. y"+4y'+4y=f(t),  y(0)=2 ,  y'(0) =…

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Q: (d) Finally, show that the conditions for the theorem are not satisfied for the initial value…

A: (D) here fx,y=y13 differentiate it with respect to x ∂f∂x=13y-13dydx initial condition y0=0

Q: 1) 3 Find the orthogonal trajectories of the family of curves y = 2x+k

A: Please see the explanation below

Q: Let y : R →R be the real-valued function defined on the real line, which is the solution of the…

A: Ans:-  Initial value problem: y'=-xy+x,  y=0=2          solution : y'+xy=x, 40=2          is of…

Q: 1. A) Find the linearization of the function at the given point. f (x, y) = 2 + x In (4 – xy), at…

A: (NOTE- These are two completely different questions, only required to do the first one. Please post…

Q: Question 1 Find and classify the critical points of the function f(x, y) = y* – 2y² – x³ + 3x.

A: The given function is: f(x,y)=y4-2y2-x3+3x

Q: 4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ…

A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

Q: 15. If g(x) and h(x) are both antiderivatives of some func- tion f(x), then what can you say about…

A: Consider that gx and hx are both antiderivative of function fx. Find gx-hx.   Since gx and hx are…

Q: 8. Find the extremum and saddle points of the function f(x, y) – x3 – 3xy + y3 if any.

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Q: Suppose that we were to model a continuous income stream using the function f(t)=t2 / (t-1)(t+1) for…

A: The function that models a continuous income stream is

Q: Theorem 17-1. If T, is a consistent estimator of y(0) and y {y(0)} is a continuous function of y(0),…

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Q: 4. Find the general form of the function that satisfies dP/dt = -3P(t).

A: A separable differential equation can be solved by separating the terms in each variable and…

Q: In problem (A), find a linear approximation f(x, y) at the indicated point. (x + y)´| at (-1,1) A)…

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Q: (4) The general solution to 7xy" – y + 10y = 0 is y = Ax x + x+ +В х + x+ x²+ x³ + and converges on…

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

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Q: the demand function for a particular beverage is given by D(q)=(3000)/((3q+2)^(2)) and if the supply…

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Q: If Σ α An diverges then E ca can diverges only if c > 0 only if c < 0 only if c+ 0 for any real…

A: Given, ∑an diverges then find for which values of c, ∑can diverges.

Q: 11. If f(r) = rª and g(r) = r³, then f' (x) = 4x³ and gʻ(x) = 3x². The Chain Rule multiplies…

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Q: Question 2 [" a. Find the critical points of the function f(x, y) = 6x² - 2x³ + 3y² + 6xy. b. s]…

A: Extreme Points of Function f(x,y)=6x2-2x3+3y2+6xy

Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a&gt;0 see below the answer and calculation

Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

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Q: (A) Suppose C= 4x²y° + i3x³y² . Find divergence of C.

A: Given complex valued field is, C=4x2y5+i3x3y2. and, ∇⇀=∂∂xi¯+∂∂yj^+∂∂zk^. Then, divergence is given…

Q: What value of b >-1 maximizes f(b) = J - x) dx!

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Q: 8. Find the extremum and saddle points of the function f(x, y) = x³ – 3ry + y³ if any

A: Given function is fx,y=x3-3xy+y3

Q: (12) Find the local maximum, minimum and saddle points (if any) of the function f(x, y) = x3 – 3x +…

A: Local maximum or minimum of the function

Q: Find the critical point of the function f(x, y) = x² + y² + xy +7.5x C=

A: To find the critical point of the function fx, y=x2+y2+xy+7.5x.

Q: 1. Find any local maximum and minimum values and saddle point (s) of the function f(x, y) = -6xy +…

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + y = f(x), y(0)…

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Q: x+2 Find the linearization of f(x) = 6 - 21 dt at x=4. 1+t 6

A: Given a function f(x) at x=4 We have to find the linearization of f(x) at x=4 For solving this 1st…

Q: 7. The function (x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree

A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…

Q: S1 xe [0,1] f(x) 0 x¢ [0, 1]

A: The given piecewise function can also be represented as, fx=10≤x≤10otherwise Solve for the mean as,…

Q: d. If x=c is an inflection point for f, then f(c) must be a local maximum or local minimum for f.…

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Q: In Problem (A), Show that f(x, y) is differentiable at the indicated point. A) f (x, y) = (x2 +…

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Q: 2. Evaluate f(x) = e3x + 2 at x = -1. Round to the nearest thousandth. %3D %3D f(-1) = ...

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Q: Find the critical number(s) of the .4 * (function f(x)=In(2x)/(3x )2 نقطة( In(2x) f (x) 3x e/2 and 0…

A: Calculus

Q: Find the critical point(s) of the function f(x, y) = -2r³ – 4ry + 2x – 5y – 1 and classify them as…

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Q: 8. Find the local maximum and minimum values and saddle points of the function f(x,y)=2x + 4y +3x²…

A: This is a problem related to maxima and minima. Please follow the procedure given below.

Q: 1. Determine the nature of the stable points of the function f (x, y) = x²y – x² – 3xy + 3x + 2y –…

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Q: 1. Find and classify the critical points of f (x, y) = 6xy – 4x³ – 3y?

A: Critical points of f will occur: fx and fy is o. Given equation is f(x,y) = 6xy-4x3-3y2…

Q: If f(x) > g(x) >0 for X in [1,0) and g(x) dx diverges to +0, then | F(x)dx also diverges to +. True…

A: It is TRUE, that 0&lt;g(x)≤f(x) for x in [1,∞)  and                               ∫1∞g(x)dx diverges…

Q: Let y : R → R be the real-valued function defined on the real line, which is the solution of the…

A: The differential equation is given as Y’  = -xy + x , y(o) = 2 From the type of the problem we can…

Q: 1)Classify the critical points of the function f(x,y)=x²+y³+x²y+4

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Q: Consider the initial value problem {y′−3y=6, {y(0)=1. What is the limit of y(x) as x approaches −∞?

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Q: If (a,B) is a saddle point of the function f(x,y)=27y2-y3+3x²-6xy, then a+ß=

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Q: 9. An equation of the line normal to the graph of f(x)=, at (1,–1) is (a) 2x - y -3 -0 (b) 2x + y…

A: Explanation: Given that  f(x)=xx-2 at (1,-1)   Concept Used: To find the normal firstly find the…

Q: Find the value of k that makes function continuous at z=4 |2z + 6 z> 4 5z – k z< 4 f(z) = ualuo…

A: Continuity.

Q: If (a,B) is a saddle point of the function f(x,y)=21y2-y3+3x2-6xy, then a+ß=

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy - + y = f(x),…

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Q: let 2.+ (3(x-1+4y+!j". ニ ): find the Critical points f f.

A: In the question we have to find critical points.