Determine Df(4, -1,6) for f(x, y,z) = ery +4zx in the direction of (-3,2,6).

Q: Which of the points P = (-1,4,-7) and Q = (6,-1,5) is closest to the z-axis? OQ (6,-1,5) OQ (6,-1,0)…

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Q: Find the Cross product of A= and B=

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Q: Find the cross product x where = 71-7j -4k and 7 = (-4,-3, 4). úxv=

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Q: Find an equation of the line through (-2, 5, 3) that is perpendicular to both u = (1, 1, 2) and the…

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Q: Find the equation y = f(x) passing through the points (-11-21), (1,15), (2,12) and (3, 3)? Find also…

A: We will use the Lagrange interpolation method. We have: x x0=-1 x1=1 x2=2 x3=3 y y0=-21 y1=15…

Q: Translate Q (0, -8) using (x, y) → (x - 3, y+ 2). Your answer: O Q'(-2, 5) Q' (3, - 10) O Q'(-3, -6)…

A: The transformation is, (x,y) ------> (x-3, y+2) So, (0, -8) ------> (0-3, -8+2)

Q: Calculate fx(l, 3) and /y(l, 3) for f (x, y) =

A: Given: fx,y=7x+y2

Q: Calculate fz(3, 6, 9), where f(x, y, z) = xyz. fz(3, 6, 9) =

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Q: Find distance between a = (3, -1, 0, -3) and b = (4, 0, 1, 2).

A: Given a=(3,-1,0,-3) and b=(4,0,1,2) and we have to find distance between a and b

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: Find point P(x,y) if it is equidistant between points A(2,9) and B(-3,6)

A: Given:-  Px,y is equidistant  from the points  A2,9  and  B -3,6 i.e,  AP=BP and  we know  that…

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: Parallel to 2x + 4y = 5, passing through (1,2)

A: The line parallel to the line 2x+4y=5.

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: Determine D,f (4,-1,6) for f(x,y,z) = ery + 4zx in the direction of (-3,2,6).

A: Given fx,y,z=ex2y+4zx3 in the direction of -3,2,6

Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: If A = ( - 1, 2) and B = (3, 4), find AB and redraw it (a) in standard position and(b) with its tail…

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Q: Find f,(2, 4) and f,(2, 4) for f(x, y) = x* + 4x?y³ + 8y*. 2.3 f-(2, 4) = f,(2, 4) =

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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.