Can you help with question 5? ad,Ame%%20Strom%20(z-lib.org).pdferstad,Ar.31 / 310%097SMO 5. (a) Find the directional derivative off(x, y, z) = xy In(x² + y² + z²).2%3Dat (1, 1, 1) in the direction given by the vector from the point (3, 2, 1) to the point (-1, 1, 2).(b) Determine also the direction of maximal increase from the point (1, 1, 1).EM 6. Suppose that f (x, y) has continuous partial derivatives. Suppose too that the maximum direc-tional derivative of f at (0, 0) is equal to 4, and that it is attained in the direction given by thevector from the origin to the point (1, 3). Find V f (0, 0).7. Let b = (bị,.Show that the derivative of f along the vector a = (aj, ., an) is b · a.ba) be a given vector and define-the function f (x) = ƒ(x1,..., Xn) = b · x.8. Let f(v) = f(v1,., Vn) denote a positive valued differentiable function of n variables definedwhenever vi > 0, i = 1, 2, ..., n. The directional elasticity of ƒ at the point v along the vectorv/||v| = a, hence in the direction from the origin to v, is denoted by El, f (v) and is, by definition,El, f(v) =|A|||| A||where f'(v) is the directional derivative of ƒ in the direction given by a. Use (8) to show thatBT321 Sp21_PS2.pdf20215-QF202-quiz. pdf20215 QF202 qui.RmdCAPM Notes.pdf2-58 PM3/12/2021ilyBANG & OLUFSdn 6ddprt scdeletehomepua144トトwnulock+backspace8.6.

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Description: Can you help with question 5? ad,Ame%%20Strom%20(z-lib.org).pdferstad,Ar.31 / 310%097SMO 5. (a) Find the directional derivative off(x, y, z) = xy In(x² + y² + z²).2%3Dat (1, 1, 1) in the direction given by the vector from the point (3, 2, 1) to the p

Given: fx,y,z=xylnx2+y2+z2 We need to find the directional derivative of the given function at point…

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(a) Find the directional derivative of f(x, y, z) = xy In(x? + y² + z?) at (1, 1, 1) in the direction given by the vector from the point (3, 2, 1) to the point (-1, 1, 2). (b) Determine also the direction of maximal increase from the point (1, 1, 1). 6. Suppose that f (x, y) has continuous partial derivatives. Suppose too that the maximum direc- tional derivative of f at (0, 0) is equal to 4, and that it is attained in the direction given by the vector from the origin to the point (1, 3). Find Vf(0, 0). 7. Let b = (b1, ..., bn) be a given vector and define-the function f(x) = f(x1, . . . , Xn) = b x. Show that the derivative of f along the vector a = (a),..., an) is b a. 8. Let f (v) = f(v1, ..., Vn) denote a positive valued differentiable function of n variables defined whenever vi > 0, i = 1, 2, ..., n. The directional elasticity of f at the point v along the vector v/|v = a, hence in the direction from the origin to v, is denoted by El, f (v) and is, by definition, %3D = (A)f "13 (A)S All %3D where f'(v) is the directional derivative of f in the direction given by a. Use (8) to show that

(a) Find the directional derivative of f(x, y, z) = xy In(x? + y² + z?) at (1, 1, 1) in the direction given by the vector from the point (3, 2, 1) to the point (-1, 1, 2). (b) Determine also the direction of maximal increase from the point (1, 1, 1). 6. Suppose that f (x, y) has continuous partial derivatives. Suppose too that the maximum direc- tional derivative of f at (0, 0) is equal to 4, and that it is attained in the direction given by the vector from the origin to the point (1, 3). Find Vf(0, 0). 7. Let b = (b1, ..., bn) be a given vector and define-the function f(x) = f(x1, . . . , Xn) = b x. Show that the derivative of f along the vector a = (a),..., an) is b a. 8. Let f (v) = f(v1, ..., Vn) denote a positive valued differentiable function of n variables defined whenever vi > 0, i = 1, 2, ..., n. The directional elasticity of f at the point v along the vector v/|v = a, hence in the direction from the origin to v, is denoted by El, f (v) and is, by definition, %3D = (A)f "13 (A)S All %3D where f'(v) is the directional derivative of f in the direction given by a. Use (8) to show that

Advanced Engineering Mathematics

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Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

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Can you help with question 5?

ad,Ame%%20Strom%20(z-lib.org).pdf
erstad,Ar.
31 / 310
%097
SMO 5. (a) Find the directional derivative of
f(x, y, z) = xy In(x² + y² + z²)
.2
%3D
at (1, 1, 1) in the direction given by the vector from the point (3, 2, 1) to the point (-1, 1, 2).
(b) Determine also the direction of maximal increase from the point (1, 1, 1).
EM 6. Suppose that f (x, y) has continuous partial derivatives. Suppose too that the maximum direc-
tional derivative of f at (0, 0) is equal to 4, and that it is attained in the direction given by the
vector from the origin to the point (1, 3). Find V f (0, 0).
7. Let b = (bị,.
Show that the derivative of f along the vector a = (aj, ., an) is b · a.
ba) be a given vector and define-the function f (x) = ƒ(x1,..., Xn) = b · x.
8. Let f(v) = f(v1,., Vn) denote a positive valued differentiable function of n variables defined
whenever vi > 0, i = 1, 2, ..., n. The directional elasticity of ƒ at the point v along the vector
v/||v| = a, hence in the direction from the origin to v, is denoted by El, f (v) and is, by definition,
El, f(v) =
|A||
|| A||
where f'(v) is the directional derivative of ƒ in the direction given by a. Use (8) to show that
BT321 Sp21_PS2.pdf
20215-QF202-quiz. pdf
20215 QF202 qui.Rmd
CAPM Notes.pdf
2-58 PM
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pua
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