If  u=sin(x+2t), then (∂2u/∂x2)=(?)(∂2u/∂t2) What is the coefficient of (∂2u/∂t2)? a) 2 b) 1/2 c) 4 d) 1/4 e) 0

Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

A:

Q: Show that if sin z| is bounded along the straight line {(x, y): ax - By = 0}, then a = 0, i.e., z…

A: In this question, we have to prove z is in real R.  here we use the property of the hyperbolic…

Q: Eualuate Je m Cz -i) dz (z-i)dz from Z =1+2i to to contour 2=

A:

Q: Show that if the function f(x, y) = ex siny + ecosx, satisfies Laplace Equation.

A: We can solve this as follows:

Q: Find the work done by a force F = 5i (mag-nitude 5 N) in moving an object along the line from the…

A: Given,

Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,-3) to (3,-9).

A: Given force is F→=xyi^+y-xj^ and straight line coordinates are 1,-3 and 3,-9

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A:

Q: 6) What is the tangent plane of f (x, y) = 5x² – 2xy? + 3xy + 4x at point (xo, Yo) = (1, –2) ?

A: The question is solved in step. 2

Q: The directional derivative of a differentiable function f(x, y) in the direction of a unit vector u…

A:

Q: dz where C denotes a 22 Contour C=2e' with a deleted onigin. (2#0)

A: For the solution of the problem follow the next step.

Q: (True/False) Suppose the work done by a force F on a particle moving along a path C is given by x,…

A: True.

Q: Determine the parametric equation for a line that is tangent (intersection) of the two fields below:…

A: We have to find out parametric equation for a line that is tangent (intersection)of the two fields…

Q: Show that ¥(x,t)= Asin(wt+kx) describes a wave motion

A: Given: ψx,t=Asinwt+kx

Q: Compute for the directional derivative of f (x,y,z) = tan (ax – 2ny)e4y-z at the point (,0, ln 4) in…

A:

Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

A:

Q: a)What is the slope of the tangent line to the curve y=2sin4x  at x=⊼(pie)/4? b) Find a unit vector…

A:

Q: Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).

A:

Q: Find the work done by the force F =xyi + (y - x)j over the straight line from (- 2, - 1) to (-1,0).

A:

Q: Let f(x, y, 2) = cos(ryz) Find the directional derivative of f at the point (,, 7) in the (a)…

A: We have to find Directional Derivative and Largest possible value.

Q: F/ prove JhaT cosh(z1+2=)=Coshz.coshaa + Sinh2,Snhze

A: Note: You have not mentioned which question to be solved. Here we are providing answer for 1…

Q: Let the the position vecor be R(t) = (e' cos(3t) , e' sin(3t),0). Compute the unit tangent vector

A: The given position vector is R(t)=etcos(3t),etsin(3t),0 . compute the unit tangent vector T(t)=?

Q: Let 0 be the angle between the line y = mx +band the x-axis. Prove thatm = tan 0.

A: The question should be :                 Let θ be the angle between the line y=mx+ b and the x-axis…

Q: af Calculate at point (-1,2) where f (x, y) = 8+ x² + 3y? dv and v = i+j. 10 2 5/2 V2

A: fx, y=8+x2+3y2  &  v=i+j Partially differentiating with respect to x, we get fxx, y=0+2x+0=2x…

Q: Let f(x,y)= e, Compute the cartesian equation of the tangent plane r,y) at the point (2.2).

A: The equation of tangent plane

Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given:        fx,y,z=xy sinz         x,y,z=1,2,π2    direction v=i+2j+2k   Differentiate the…

Q: Find the work done by the force F= xyi + (y - x)j over the straight line from (1,2) to (3,6).

A: we have to find the work done by the given force

Q: Determine the equation of the tangemt line to c(z) = cot (Tz)sin-1(z) at the point where z=1/2.

A:

Q: cotu. vX + vy + y %3D If u = show that x ax ay = CoS coS х - у

A:

Q: Show that UV=12 given, UX = 8, and XY = 10 using the intersecting %3D Secant-Tangent Theorem. * U

A:

Q: Show that whether if the co-vector w can be written as dø differential? w = y. (x +). dx + x. (+).dy…

A: Given:  w=y·x+y2· dx+x·x2+y·dy....(1)

Q: If, for V = V (t), tsin(V) = cos(V)+ In(t), then: a) V'(t) = 1 – tsin(V) t(t cos(V) + sin(V)) b)…

A:

Q: Uzz + Uyy = u %3D tt u(г, у, 0) — 0 и (х, у, t) — 2? -у?

A: In this question, we have find the velocity of the membrane at given time and point.

Q: 2л where a, b > 0. dx = - ile* + b Prove that %3D

A:

Q: The directional derivative of f(x, y) = xe + cosxy at P,(2,0) in the direction of the vector 3i - 4j…

A:

Q: Let f(x, y) = sin(cy). Then the directional derivative of f in the direction of the vector at the…

A: fx,y=sinxy We have to confirm whether directional derivative of f in the direction of the vector…

Q: 2dy -2y 2. zt at

A: Solved below

Q: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

Q: Find the work done by the force F= xyi + (y - x)j over the straight line from (-1,- 2) to (2,1).

A:

Q: Find the directional derivative Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an…

A:

Q: The unit tangent vector of a(t) =cos 2t e, +stn 2t e, - tez at t = is

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: In R', Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the…

A:

Q: The directional derivative of f(x, y, z) = x? + y? + 4xz at Po(1,-2,2) in the direction of the…

A:

Q: Show that if |sin z| is bounded along the straight line {(x, y) : ax - By = 0}, then a = 0, i.e.,…

A: We know, sin z = sin x cosh y + i cos x sinh y, Where, cosh and sinh are hyperbolic functions.

Q: Find the work done by the force F = 4xyỉ + (2x2 - 3xy)j by pushing a particle along the line segment…

A: Step:-1 Given Force is F→ =4xy i→ +2x2 -3xy j→ Here, given that particle moves along the line…

Q: Prove that the directional derivative of flay.2) = aysinz. direction v=i +2j+2k 1Is Sin Z at…

A:

Q: The length of the path describe by the parametric equations, x=(1/3)t^3 and y=(1/2)t^2, where 0≤t≤1,…

A:

Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.