Find the image of the point (-2,4) under a shear of factor 5 in the y- direction. (2, 6) O (2, -6) O (-2, -6) O (-2, 6)

Q: How is linear approximation used to approximate the value of afunction ƒ near a point at which ƒ and…

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Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: Calculate the distance from the point (4,−2,7) to the plane x−3y+5z=−8.

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Q: Find the minimum distance from the point (2, -1, 1) to the plane x + y - z = 2.

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Q: Sz sec2ysin4ydy

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Q: Find the distance from the point (−3,0,2) to the plane - 3x + y + 5z = 0

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Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: What is the maximum slope of f(x,y,z)=yex-x2sin(z) at the point (0,7,5)?

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Q: What is the maximum slope of f(x,y,z)=ye^x-x^2sin(z) at the point (0,7,-3)?

A: Given the function fx,y,z=yex-x2sinz and the point 0,7,-3. Computing the partial derivatives,…

Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

Q: Find the minimum distance from the point (6, 0, 9) to the plane x – y + z = 5. (Hint: To simplify…

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Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: Find the minimum distance from the point to the plane x- y +z = 6. (1, -6, 2)

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Q: Find the gradient of a normal line to the parabola y=x^2+5x-9 at the point (1,1)

A: In this question, the concept of slope is applied. Slope A line's slope or gradient is a number that…

Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

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Q: Find the gradient of the function at the given point. In(x? - y) - 3, (2, 3) Vz(2, 3) -

A: We have to find the gradient of the function z = lnx2-yx-3 at the point 2, 3.

Q: Find the minimum distance from point (2, 5, -1) and plane 3x + 4y + z = 10.

A: Given query is to find the minimum distance.

Q: Find the distance from the point (2, 0, 0) to the plane x + 2y + 2z = 0.

A: Given a point, (2, 0, 0) and the equation of the plane x + 2y + 2z = 0.

Q: Consider a closed rectangular box with dimensions xx  ft by  yy  ft by zz ft. If xx  is increasing…

A: Proceed as shown

Q: Find the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius…

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Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

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Q: find the distance from the point to the plane. (1, 0, -1), -4x + y + z = 4

A: Concept -Let the equation of plane be -Ax+By+Cz+D = 0And the coordinates of a point be - (x1, y1,…

Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Find a set of symmetric equations for the normal line to the surface xyz = 12 at the point (2, −2,…

A: The normal line to the surface xyz = 12 at the point (2, −2, −3).

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: Find the point P nearest to Q = (−1, 3, −1) on the planex − 4z = 2

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Q: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

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Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

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Q: What are the coordinates of the points in the graph of y – z² + 6z – 13 = 0 in which the tangent…

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Q: Make the cubic y = ax3+bx2+cx+d pass through the points (0,-6), (1,-2) and be tangent to the line…

A: This is the simple question based on algebra and derivative which could be solved using the basic…

Q: Find the shortest distance from the point (0,2,3) to the plane x+2y+z=1

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Q: Find the distance between the point (3, 1, −2) and the plane x + 2y − 2z = 4.

A: Given,             Point  (3, 1, −2)          Plane   x + 2y − 2z = 4

Q: Find the gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2

Q: Find an equation of the tangent plane to the surface at the given point. 5x2 + 2y2 + 5z2 = 73,    P…

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Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

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Q: Find the distance between the point (3,11,-2) and the plane X t 2y

A: Explanation of the answer is as follows

Q: Find symmetric equations of the normal line to the surface 3xy-z = 0 at the point (-4, -2, 24). O…

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Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

A: A parametric curve is a normal curve where we choose to define the curve`s x and y values in terms…

Q: Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5…

A: Given: fx,y=4xy9-72x-9y vertices 0,0 18,00,1

Q: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

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Q: Find the points on the cone z2 = x² + y2 that are closest to the point (8, 2, 0).

A: we have given the equation of cone z2=x2+y2 and the point (8,2,0)to…

Q: find the slope of the tangent to the curve of intersection between 6z=3squareroot(20-x^2) and the…

A: the cylinder equation is given by  and the plane is given by  We want to define each variable in…

Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: Find the distance between the planes  5x − 3y + z = 5  and  5x − 3y + z = −9.

A: Two planes  and will always be parallel if The given planes  and  are parallel because we can see…

Q: Find the distance from the point to the plane. (3, 0, 10), 2.x + 3y + z = 2

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Q: Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A: This is a problem of geometry. We will calculate slope of x, y and z at given point and general…