et e2(x+2) dy A dz + e¯Y dz ^ dæ + ez-2) dæ ^ dy W = e a two-form on R³, and ø : (R>0)² → R³ be the smooth function $(u, v) = (In(uv), In(u + v), In(uv)). ind ø*w. du Л dv

Q: Check is bilinear form IR OY not? an

A:

Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

A:

Q: f(x,y,z) be a differentiable function the point P(2,5,-1). Let at Which of the following is the…

A: Answer is mentioned below

Q: The tangent plane to the graph of the function f(x, y) = ey at the point with x = 1, y = -1, a) has…

A: Equation of the tangent plane to the surface

Q: The directional derivative of o = xy²z+ 4x'z at (-1,1,2) in the direction 2i +j- 2k. ans. 38 - 38 3.…

A:

Q: a) Sketch the graph of 7(t) =and show the direction of the increasing t, where 0 c) If 7(1)…

A: The vector field is rt=cost, t, sint. Now, if yt=t, then x=cosy and z=siny. Thus, the vector field…

Q: 2. Draw a contour map of function f(x, y) = 2x/(x² + y²) showing several level curves.

A: We Know that  The level curves of a function f of two variables are the curves with equations f(x,y)…

Q: The divergence and curl of the functionf(r,e,p) = (r sec 0)e, O (4r^(3 ) sec®)er O None of these.…

A: Topic:- vector algebra

Q: Q4\ Graph the curve r=1-cosx in Cartesion xy - plane

A:

Q: 6. Tangent Plane dro find an equatin the Plane and a set Line equatin g tho of Tangent * 9 o the…

A: We have to find the equation of tangent plane and set of equation of the normal line to the given…

Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

A:

Q: За and the equation of the tangent line to the curve at the point (a,b) is y = 2 - If f(x) = -x- x +…

A:

Q: Let h be a differentiable function of x obtained from the parametric equations a = f(t), y= g(t) .…

A: if x=f(t) and y=g(t) thendydx=dydtdxdt

Q: Evaluate -I doc ezx ď'cax +2) where d'cax) is the derivative of S lx) delta function

A: Given :           ∫-∞-1dx e2xδ'(x+2)

Q: Evaluate d:/dx on the surface x: + + x²y®=² = 3 at the point (1, 1, 1).

A:

Q: »[32° dx = 3x² A) 6 B) 7 C)8 D) 9 타 10 xdx A) - B) - Suppose F and G are continuous functions with…

A: We have to answer the following...

Q: Consider a differentiable function p(x,y) with the properties below. Use these properties to answer…

A:

Q: Let w = e®(z+=) dy ^ dz+e" dz ^ dæ + e(z =) dæ A dy be a two-form on R³, and o : (IR>0)² → R³ be the…

A: Given: A two-form on ℝ3, ω=e8x+zdy∧dz+e-ydz∧dx+e6x-zdx∧dy A smooth function ϕ:ℝ>02→ℝ3, where…

Q: iv is analytic = -11..

A:

Q: determine wave direction in the function f(x,y) x^y — x²y³ decreases faster at the point (2,-3)

A: Wave direction in the function f(x,y)= x4y-x2y3 that decreases faster at the point (2,-3) is…

Q: 3. Show the limit x+y lim (x,y)-(-1,1) x+1+iny does not exist.

A:

Q: du du dx' dy 1) u = 3x²y + xlny² - Inxy 2) u =xe*Y+ ‡ ArcTan , 3) u = +2²-3² I. Find and (whenever…

A:

Q: Differentiation [SND] If y = (r+ v1+x²)", prove that, (1+2²) 2 +ry - m²y =0

A:

Q: Hi, I need help using implicit differentiation to find an equation of the tangent line to the curve…

A: To find the slope of the tangent we need dydx at x=3 and y=1…

Q: Evaluate ∮C (x + 3y)dx + ydy where C is the Jordan curve given by the graphs of y = e^x, y = e^−x…

A: ∮Cx+3ydx+ydy Where C:y=ex, y=e-x, y=e-1

Q: Jo Jo JoT f(x, y, x) dy dz dx is a function in terms of z-

A:

Q: f a functiar derivatives z=f(x*, 2ayl -x) tikle u=xZ and W= 2 xy%-X we get 2=2x fu" (2y* -1) · fw t…

A:

Q: 40. Regression analysis makes use of the relationship between two or more quantitative variables so…

A: ...

Q: Evaluate S (* + 7)i + (2») 5).dF. where Lis the quarter-circle with parametric form z = cos (t) and…

A:

Q: Let Find o*w. w = e e6(x+²) dy ^ dz + e¯ª dz^ dx + e¹(x−²) dx / dy be a two-form on R³, and 6:…

A: Given: A two-form on ℝ3; ω=e6x+zdy∧dz+e-ydz∧dx+e4x-zdx∧dy. A smooth function, ϕ:ℝ>02→ℝ3 defined…

Q: Find the length of the curve 2 ܐܨ 1, a² 6² from the point (a, 0, 0) to the point (x, y, z). x = a…

A: The equation of the given curve is x2a2-y2b2=1, x=acoshza To find the length of the curve from the…

Q: If we discuss the derivative of the function f(z) = z. Imz by Cauchy- Riemann equations. we see fz)…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 1. The following equation shows your retained information depending as a function of the hours of…

A: we have been given the function for retaining information as a function of t -'hours of study'…

Q: Use imp licit differentiation to find the slope of ngent line to the curve defined by the tar…

A: