22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of vecfor U = 2€ +j-2k-

Q: Compute the work done by the force 7 = (sin(x + y), xy, x²z) in moving an object along the…

A: Given force The object is moving along the straight line and from

Q: Find an equation of the line tangent to the intersection of the cylinders x² + z² = 4, y² + z² = 4…

A: The parametric form of the tangent line is  x=x0+aty=y0+btz=z0+ct where, (a,b,c) is the direction…

Q: Q1: Find the derivative of f(x,y,z)=x^2+xy^3-z at point P_o (1,1,0) in the direction of vector V…

A:

Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

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Q: The equation of the tangent plane of the graph of function z = xy + 2x² - y3 at point (2, -1) is

A:

Q: Find one normal vector of the tangent plane to f(x, y) = cos(x² +y²) at point P(1,1, cos 2).

A: As we know the expression of the normal vector to the tangent plane at a point on the curve can be…

Q: a) Use a power series to approximate the definite integral, I, to six decimal places. SHOW ALL WORK.…

A: Solution:ConsiderI=∫00.5ln (1+x4)dxTo find the series approximation to six decimal places using…

Q: Q/ Solve the di Pferential e quation y+2y-3y=7R-3x

A:

Q: Let f(x,y,z) = x ^3+2yz-z^2 What is the steepest directional slope at the point (1,1,1)

A: Given function is  fx,y,z=x3+2yz-z2

Q: Find the directional derivative of f (x,y,z)=xy² +ze?»-6 in the direction of v = 6i– 3j+2k. 8)

A:

Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

Q: [3 0 0 1 Lo 0 -1] Suppose that A is a matrix such that (A+I)1 Then a. A 1. Lo o b. We can not find A…

A:

Q: What are the coordinates of V'

A: For Triangle ∆TUV, the coordinates at point T is (-7,-6) at point U is (-8,3)  and at point V is…

Q: Find a vector that is perpendicular to the surface 4e^{(z-1)}+x^{2}y=xyz at the point (−1,−2,1).

A: Given the surface :

Q: Find speed and acceleration at a point (C,D), if distance of a particle is given by S = 2t^3− 3t^2…

A: The acceleration of an object is the rate of change of its velocity. The velocity of an object is…

Q: Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).

A: The linearization of a function f(x,y,z) at a point (a,b,c) is given by the expression;…

Q: 5. What are the coordinates of the JNBS if J'(-2, 4), N'(3, 5), B'(2, 3), and S'(0, 2) after R(90".…

A: Given: J'(-2,4) , N'(3,5), B'(2,3) and S'(0,2)

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: The tangent plane to the surface 2x² + 3y² = 5z² at (1, 1, 1) has an equation ax +by+cz = d.What is…

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Q: Find the solution of the given initial value problem. X = -2t е (2) e- ² + (3) ¹0 ° +- ()~²¹ - () ¹²…

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Q: What is the rate of change of the function f(x,y) = ye^(2cos x) + tan(x+3y) at ( 3π/2 , π/2) in the…

A: Given: fx,y=ye2cosx+tanx+3y To Find: Rate of change of fx,y in the direction of the vector 3,4 at…

Q: Find the parametrization of the curve defined by the intersection of the two surfaces y = x^2 − 3z^2…

A:

Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

A: Given that

Q: 5. Find all analytic functions f such that Ref + Im f = ry.

A: We need to find the analytic functions f such that Re f+Im f=xy. Consider the function of the form…

Q: Evaluate F dr where F(x, y, z)= (x', y’, xyz) and C is the line segment from х, у, со (1, 4, 3).

A: Use parametric to solve

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.