At the point P=(4,1) in the direction v =(i +j )/sqrt2, the directional derivative is approximately

Q: The derivate of position is velocity, the derivative of velocity is acceleration.

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Q: Let h(x, y, z) = ln(x² + y² + z²). (a) What is the direction of maximal increase of h at the…

A: Given function:  hx,y,z=lnx2+y2+z2 To find: a) Direction of maximum of h at the 1,1,1. b) The…

Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: How can you use directional derivatives to estimate change?

A: Let f be a differentiable function. The directional derivative of f in a particular direction at a…

Q: Assume that w = f(s3 + t?) and f'(x) = ex. Find dw dw and at ds dw at dw

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Q: If f(t) = t^2 - 5t + 4 represents the rectilinear motion of a particle, the particle changes…

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Q: f (x, y, z) = arctan(x² + 2y + z) At the point A(0,1,0) along the direction ñ, where n is the…

A: Given that f(x,y,z)=arctan(x2+2y+z)  For a function of three variables f(x,y,z), the directional…

Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: Calculate the derivative at the point (0,0) of the function given by the equation x=y−2siny.

A: We differentiate both sides with respect to x

Q: The derivative of ƒ(x, y) at P0(1, 2) in the direction of i + j is 2sqrt(2) and in the direction of…

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Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: u = cos 0 i + sin 0 j cuando (a) 0 = 00 y

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Q: Find the maximum rate of change of f(p, q, r) = arctan(pqr) at the point (2, 6, 2).

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