For each of the following functions ƒ :R² →R compute at the point a. sin(x)cos(y) (a) f(x,y) = a = (- 3' 4 (b) f(x, y)=ev2-y; а (1, 1) 1 (c) f(х, у)%3D a = (-4, 3) (x, v)||"

Q: Consider the one-form y4 W = dæ + (4 ln(10x)y³ + 13y) dy on {(x, y) E R² | x > 0}. If the one-form…

A: Given: The one-form…

Q: dw Find the value of- dt at the point (1, In 2 ,0) on the curve x = cos t ,y= sin t, 0 <t< 2n where…

A:

Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

A:

Q: B: Expressand as functions of u and v both by using the Chain Rule and by expressing z directly in…

A:

Q: Let A E R"Xn, let b e R", and let n n f (x) = xT Ar + 6Tx = Aikr;xk +> b;x;. i,k=1 i=1 Show that f :…

A: Definition: A function f:ℝn→ℝm is differentiable at x0 with derivative M if M:ℝn→ℝm is linear and…

Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

A:

Q: If sin(x) f(x)= 68+t2 dt Jtan(x) and g(y)= f(x) dx , Then g) is equal to

A:

Q: Let f(x) = e2sinz 1. Use the local linear approximation of f at x = 0 to approximate e2 sin(0.01

A:

Q: Given f(z) = | t2 – 16 dt 1+ cos²(t) OS At what value of a does the local max of f(x) occur?

A:

Q: Find the particular antiderivative of the function f(x) point (0, –1). e" (2ª – 1) whose graph…

A:

Q: Find a non-zero function h for which F(x, y) = h(x)(x sin y + y cos y)i + h(x)(x cosy – y sin y)j is…

A: Given vector field is, Fx,y→=hxxsiny+ycosyi+hxxcosy-ysinyj.

Q: dy For the function dt d y is 3 cos t, the third %3D order derivative dt3 O 3 cos t

A: Given: dydt=3cost To find the third order derivative d3ydt3. Solution: We have, dydt=3cost…

Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show…

A: Given: w=fx,y, x=rcosθ, y=rsinθ If w is a multi variable function w(x,y,a,........z) thus the…

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e-t and z = r²s sint, find the value of du/ds and au/ar…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

A:

Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: Find aw/as and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) X = s + t, y…

A: we have to find partial derivative by using chain rule

Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

A:

Q: Let y = f(x), where %3D 7 f(x) = x + Find the differential of the function. dy =

A:

Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: Find dz/dr if z as a two variables function in r and y is defined implicitly by y3 + x22 + r sin r…

A:

Q: dz at t = dt if z = f(x, y) = x² – 3xy+ 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t. Use chain…

A:

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

A:

Q: Consider the function 23 – 3y if (x, y) # (0,0), f (x, y) = x² + y? if (x, y) = (0,0). Show that…

A:

Q: Find the linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: Let y = f(x), where f(x) = 3x+6/x+6 Find the differential of the function. dy =?

A:

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

A:

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

A:

Q: Find the differential and evaluate for the given x and d/x of the function, y = 3x2- x+ 6, x = 2, dx…

A:

Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

A:

Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

Q: dw at t= dt For the functions w = - 4x + 10y, x= cos t, and y = sin t, express as a function of t,…

A:

Q: Find where y(x) is defined by d²y dr? (a) 3x2 – e2, (b) sin 3x + cos r, (c) 1+x – x2 + In r. - -

A:

Q: The function f(z) = 1 has a poles at z = %3| ez – 1

A:

Q: Let y = f(x), where 3x? f(x) : Зx + 4 ,2 x + 4 Find the differential of the function. dy =

A:

Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: (i) Find the linear approximation of the function f(x, y) = 1 - xy cos πy at (1, 1) and use it to…

A: Here, the given function is: f(x,y)=1-xycos πy To find the linear approximation of the function. For…

Q: For f(x, y)= e sin(25x), evaluate fy at the point (77, 0). Of,(7,0)=50 O fy(7,0)=0 Of(7,0)=51…

A:

Q: Find In(y') at the point (0, 1/e) where xy° – In(xª + y) = 1.

A:

Q: 51. grad f = (2x + 3e")7 +3xe'j

A:

Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

A:

Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

A:

Q: cos(x) If f(x) = ["(@) "g(x) V1 + t3 dt, where g(x) = S [1 + sin(t²)]dt, find f'(;). 1 %3D

A:

Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

A:

Q: ind the linear approximation of the function at the given point. x_ v) = -4 sinx+ 7 cos y at (0, 7…

A: Hey, Since you have posted multiple questions we will answer only first question.

Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

A:

Q: Verify the linear approximation at ( 0, 0) for e^x cos(xy)

A:

Q: Find the directional derivative of Du f(2,1) in the direction of: d = 7i + 2j To f(x, y) = In(Ges…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…