Use the Lagrange multiplier method to find the stationary value(s) of z given by z = xy + 4x-3, subject to x + 3y = 8. The unique stationary point is given by X* = y* = X* = 1 A/ A

Q: Find ∂y/∂x1 and ∂y/x2

A:

Q: √²³₁(−12xy² + 8x³y + 3)dxdy

A: LetWe have to evaluate the above integral.

Q: (x+y)^2=x^2 + 2xy + y2, subsitute (-2) for x,and (-1) for y, and check if the left hand side is…

A:

Q: 7. fox)=x-x-2 fix) = R²+2x3 %3D

A:

Q: b) Find the slope of the function f(x) = VI+1at point (15,4).

A: The slope of  f(x) at a point (a,b) or x=a and f(a)=b is given by, df(x)dxx=a or f'(a)

Q: An established rollercoaster can be modelled by f:[0,3]--> R, f(x) = -x^3+3x^2-x+5, where x-axis…

A: The problem is asking us to find a parabolic function that extends the existing rollercoaster track.…

Q: Verify by differentiation that x4 is an antiderivative of 4x3.

A:

Q: 4) Find the orthogonal trajectories of the family of curves

A:

Q: = Use the graph and the given equations, f(x) = 5x² (red) and f(x) = to support your response to the…

A: We have to use integral to find area bounded between curves or line .

Q: Find the best quadratic approximation, Q(x, y) of V9 + 7x + 5y for (x, y) near (0,0), Q(x, y) :…

A:

Q: 3. a) Use REGRESSION to find a quartic function y = ax* + bx3 + cx² + dx + e that fits the data. b)…

A: given y=ax4+bx3+cx2+dx+eUsing the regression to find the quadratic function

Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

A:

Q: Given the function g of the two real variables t and u by g(t,u)=t^2 + tu-u^2+(6+2)u c) Determine…

A: Linearization of a function g(t,u) about (a,b) is  L(t,u)=g(a,b)+(t-a)gt(a,b)+(u-b)gu(a,b)

Q: Suppose a firm's technology is represented by the production function f(L, K) = min(L, 2K), where L…

A: As we know that all isoquant curves are strictly negative sloped hence, if one of the point is (4,…

Q: Find dx (9x² + 16 1 1 - In |3x + V16 + 9x²| + c -In |3x – V16 + 9x²| + c Option 2 Option 3 1 1 In…

A:

Q: 2. Find the equation of the place that pusses + through the point= (-1,2,1) Contains the line of…

A:

Q: Use Lagrange quadratic polynomial to estimate the value of y at x = 1.5 from the data points (0,…

A:

Q: hich of the following could be the grapl y=x^(2)+2x+2?

A:

Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

A:

Q: Evaluate: (8t3 – 9t2 + 7)dt -

A: Topic = Integration

Q: Find two linearly independent solutions of 2x²y" - xy + (-4x + 1)y=0, x > 0 of the form y₁ = x¹(1+…

A:

Q: Find the orthogonal trajectories of

A: Given,          y=ax2+4ax+4a, where a being paarameter.

Q: Consider the quadratic function V(x)= ax +bx + cx +2x,x, -4x,x, -2x,x,, try to find the range of…

A:

Q: (x² + 1)ª (2.x + 1)3(3x – 1)5 y =

A: Simple differentiation problem....

Q: If A = 3a_0 + 2a_0 - 5a_z and B = -2a_p + 3a_0- a_z are given at points P(3,T1/6,5) and Q(4,T1/3,3)…

A:

Q: identify the coordnates of any local maximum or minmum values of the function y=(x+3)2/ e2x

A: y=(x+3)2/ e2x Or, y = (x+3)2e-2x We need to find it's derivative and equate the same to zero.