In the Cartesian plane below, AB and CD are parallel linear functions. У (ст) A(0,24) |c E(8,3) D в (32,0) >x (cm)

Q: If W[y,, Y2 Y3]=0, then {y1, y2 , y3} must linearly dependent, where y1, y2 , y3 are diffferentiable…

A: To find- If Wy1, y2, y3 = 0, then y1, y2, y3 must linearly dependent, where y1, y2, y3 are…

Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: Find the exact value of Duf(-2,-1,-3) in the direction of v = 3i+ 4j + 5k for the function f(x,y, z)…

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Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: Find the following statement is true? ' W[y1,y2] = 0 implies y1 and y2 are linearly dependent'

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Q: Find the linearization at the point indicated:   V (h) = 4h(2 − h)(4 − 2h), a = 1

A: Given: Vh=4h2-h4-2h ,a=1

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) %3D Vf(4, 2) =

A: If f is a function of x and y then gradient of f is given by ∇f=∂f∂xi^+∂f∂yj^So, ∇fa,b is given by…

Q: Find the linearization L(x,y) of the function at each point. f(x у) — х2 + у2 +1 а. (1,1) b. (4,2)…

A: Solve the given function

Q: Find the equations of the normal x2+ y2 = 1 at the point (2, 1). A) x = 2y в) х+у31 c) 2x + 3y = 3…

A: First find the slope of normal and then use the given point to find the equation of normal.

Q: Determine the linear dependence of fi(t) = t + 2, f2(t) 2t2 + 3t, and %3D II f3(t) = -t2 +3.

A: Given functions are f1t=t+2f2t=2t2+3tf3t=-t2+3 To determine whether f1,f2,f3 are linearly…

Q: find the trace of the plane in the given coordinate plane.  −x + y = 4, xz

A: Find trace of the plane in the coordinate plane -x+y=4 in xz

Q: Find the gradient of the function w = 2x²y - 4yz + z² at the point (1, 1, -2). ○ 2î+ 10j - sk Ⓒ41+…

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Q: iven T: R2 -> R2, where T(x,y) = (x,y2), Is T linear? Explain.

A: Given: To explain the given statement as follows, R2 + R2, where T(x,y) = (x,y2).

Q: Q1. Find the linearization of f(x, y)= x² – xy + 12y? +3 at the point (3, 2).

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Q: a) What is the dimension of {(x, y) E R² : x + y = 0}?

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Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² + 1 a. (4,1) b. (2,4)…

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Q: Find an equation of the plane with x-intercept = 5, y-intercept = 8 and z-intercept = 3. O Sx + 8y +…

A: In the given question we have to find the equation of the plane such that the plane intersect at…

Q: Let f(x, y) = x² – y?. Find (c) The linearization of f at the point (2, –3).

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Q: Find the gradient of the function f(r, h) = 2xrh + xr² at the point (2, 2). V f(2, 2) =

A: Given,   f(r,h)=2πrh+πr2

Q: The gradient of the functiong(x, y, z) = In a In y In z at the point (2, 4, 3) is:

A: Given, g(x, y, z)=lnx lny lnz

Q: Compute the gradient of the function at the given point. f(x.y) = - 4x + 9y, (-8,-4) O A. - 256i -…

A: Solve the following

Q: Find the gradient of the function at the given point. In(x² – y) – 6, (2, 3) z = Vz(2, 3) =

A:

Q: Find the gradient of the function: f(x, y, z) = x'y + = OF = (7x + 6x°)i + 3y²j + k %3D OF = 7x°y°i…

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 5y + 4, (3, 2) %3D Vf(3, 2) =

A: We will solve the problem.

Q: Find the gradient of the function w = 2x²y – 4yz + a at the point (1, 1, -2). O 2i+ 10j- 8k O 4i+…

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Q: Find the gradient of f(m, n) = m³ +n³. grad f = i +

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Q: Determine values of x and y so that v · w = 0 and v · u =

A: There are vector representation given as, v=x1y , w=x-20  and u=0-9y. To find the value of  x  and y…

Q: Check that the functions f(t) =t and g(t) = e ^ t are linearly independent or not.

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Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) = %3D

A: To find the gradient of the function at the given point.fx, y=5x+2y2+4, 4, 2∇f4, 2=?

Q: If W[y, , y2• Y3]=0, then {y1 , y2 , y3} must linearly dependent, where y1 , y2 , y3 are…

A:

Q: The gradient vector of the function f(x, y) = ln(xy) — x³ at the point (-1, 1) is (-1,-2). Select…

A: This question is based on gradient of function at a point.

Q: Differentiate the follo ear and non-linear. w +z =2 1. x +y- z= G X +v-

A: (i) First we differentiate the given equation with respect to x: xy+z=2⇒ddxxy+z=ddx2⇒y+xdydx+dzdx=0…

Q: O Find the orthogonal trajectories of the circles a2 + (y – c)² = c², c+ 0 - %3D

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: What is the symmetric equation of the line that is normal to the plane x + y + z = 9 at the point…

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Q: Find the gradient of f(x,y,z) = (x² + y² +z²) ¯ - 1/2 Vf(-21.-2)=(1+Dj+k (Type integers or…

A: topic - gradient of a function

Q: Find the gradient of the function at the given point. w = 5x²y-7yz+z², (1, 1, -2) O 15i+ 26j+ 11k O…

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Q: Find the gradient of f(x,y,z) = (x² + y² +z²) Vfl (2,-1,-2)=(₁+j+k (Type integers or simplified…

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Q: Let f (x, y , z) be a function with gradient vector . What is the point of extreme value of f with…

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Q: 2. Evaluate (3xy+iy²)dz along the straight line joining z = i and z = 2 – i.

A: Given the Integral, ∫i2-i(3xy+iy2)dz We, know that z=x+iy ⇒dz=dx+idy, When z=i    ⇒x=0 and y=1  When…

Q: Choose the gradient of f(x, y) = x²y³. (a) 2xi +3y²j, (b) (c) 2xy³i+3x²y²j, (d) x²i+y³j, y³i+x²j.

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Q: 8. xyzx +2y³ (z, = 1

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Q: The points P (x1, y1), Q(x2,y2) and R (x,y) are collinear. Use the gradient formula to show that…

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Q: Find real numbers x, y and z such that (а) (b) 7xi + (y – 3)j + 6k = 10i + 8j – 3zk (x + 4)i + (y–…

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Q: Find the values of ∂z/∂x and ∂z/∂y at the points z3 - xy + yz + y3 - 2 = 0, (1, 1, 1)

A: Given: z3-xy+yz+y3-2=0  At the points (1,1,1) To find: The values  of ∂z∂x and ∂z∂y.

Q: Evaluate fcF. dr where F = ( 3 z – y)i + (2 x +2 z)j + 2 z k along the straight line from (1,1,2) to…

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Q: Evaluate A dr where C is the line joining (0, 0, 0) and (2, 1, 1), given A= (2y + 3)I +xj+(yz – x)k.…

A: # given A=(2y+3)I+xzj+(yz-x)k  Then to find integral(A*dr) from (0,0,0)to(2,1,1)

Q: Determine whether the functions y1 and y2 are linearly dependent on the interval (0,1)

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Q: . Find the linearization of √ x at a = 49. Then use your linearization to approximate √ 56.

A: I am going to solve the given problem by using some simple calculus  get the required result.

Q: I – 1 f(r) = I +1 f(x): that are parallel to the line x – – 2y = 2.

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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.