When calculate the directional we derivatives of the function f(x,y,z)=x2 +y +z° at the point (1,1,1) in different directions, which of the following value(s) can we obtain? I:-6 II:-4 Ш:1 IV:5 V: 7 (a) I, II, III, IV, V (b) I, I, Ш, ГV (с) 1, Ш, IV (d) II, III (e) Only III

Q: 1. a. Find the maximum magnitude of directional derivative of f(x, y) = ln(x³ +y³) at the point Po =…

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Q: A function z=f(x, y) is defined implicitly by the equation xy2 - x²z+yz² -z = 11 near point (2, -2,…

A: Given function is fx, y, z = xy2-x2z+yz2-z-11

Q: Find the directional derivative of the function at the point P in the direction of the point Q. f(x,…

A: The function is given as , fx,y,z=xy-xy2z2 find the directional derivative at point P1,-2,1 in…

Q: 3. Find the value of the directional derivative at the particular point Po for the given function in…

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Q: Compute the directional derivative of f(x,y) at the point P in the direction of the point Q. f(x,y)…

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Q: 4–6 Find the directional derivative of f at the given point in the direction indicated by the angle…

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Q: Q3/ Find the directional derivative of the function f(x,y,z)=xy+yz+zx at the point Po(1,-1,2) in the…

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Q: Find the directional derivative of f(x, y, z) : 4y at P(3,1, –2) x + z in the direction from P to…

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Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) : x2 + y2 + z? (7,…

A: Formula for the directional derivative of the function f(x,y,z) is: ∇f = fxi +fyj +fzk Where…

Q: Find the directional derivative of f(x, y, z) 2y at P(5, 2,-4) in the direction from P to Q(4, 3,…

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Q: 3. Find the value of the directional derivative at the particular point Po for the given function in…

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Q: At the point P(1,2, 3), a function f(z, y, z) has directional derivative of-4 in the direction…

A: We have to find the value of fy(P).

Q: Find the directional derivative of the function at P in the direction of v. F(x, y) = x³ - y, P(8,…

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Q: Find the directional derivative of f(x, y) at P(5,0) in the %3D x + y direction of Q(3, –3). NOTE:…

A: Given- f(x,y)=20xx+y To find the directional vector of f(x, y) at P(5,0) in the direction of…

Q: 6. (a) Let f(x, y) = x³y*. Find the directional derivative of f in the direction of T = (3, 4) at…

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Q: Find the directional derivative of f(x, y, z) = x² + y² - z at P:(4,1,-17) in the direction of a =…

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Q: Find the directional derivative of f(x, y) = 5e-y at (-1, 1) in the direction of (-4,3). %3D

A: The directional derivative is the dot product of the gradient at the given point and the normalized…

Q: What is the directional derivative of the function f (x, y) = 2xy- 3y2 at point po- (5,5) in the…

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Q: Suppose that f(x, y) = x°y. The directional derivative of f(x, y) in the directional (– 2, – 1) and…

A: Explained below

Q: Find the gradient of the function at the given point. Function Point f(x, y) = x² + 2xy (4,0) Vf(4,…

A: Given :Function : fx,y=x2+2xy

Q: Find the directional derivative of the function at point P in the direction of v. 3 u = 4 f(x, y) =…

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Q: Find the directional derivative of f(x, y) = x/y at the point P(1, −4) in the direction of v =

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Q: (i) Find the directional derivative of f(x, y) at the %3D 2 2 x +y point (1, 2) in the direction of…

A: As we know that the expression for the directional derivative is: D.D=∇fPx,y·vv Given: fx,y=xx2+y2 ;…

Q: Calculate the directional derivative of the function f(x.y.z)= In(xy+xz+yz) at (1, 1, 1) in the…

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Q: Compute the directional derivative of f(x,y) at the point P in the direction of the point Q. 2…

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Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: The given scalar field is - f(x,y,z)=(x^2)z+(y^3)(z^2)-xyz

Q: 1. Let f(x, y) = x cos(2x + y). a) Find the value of the directional derivative of /(x, y) at| in…

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Q: Evaluate the directional derivative of the function f=x^2-y^2+2z^2 at the point A (1,2,3) in the…

A: Point A(1,2,3) and Point B(5,0,4) ⇒AB→=5-1i^+0-2j^+4-3k^=4i^-2j^+k^ Now we have to find the…

Q: 4) Find direction derivative f(x, y) = x2 -3xy at the point (-1,2) in the direction 0 %3D 6

A: The directional derivative of a function f(x, y) is given by Du.fx,y=fxx,ya+fyx,yb where u.=a,b is a…

Q: The directional derivative of 2e" cos y at f(x, y) = -2e* cos y at (0, 7) in the direction of v =…

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Q: Find the gradient of the function at the given point. Function g(x, y) = ye-* Vg(0,4)= Point (0,4)…

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Q: 24. f(x, y, z) = xy² z³, P(2,1, 1), Q(0, –3, 5)

A: Given function is   f(x,y,z)=xy2z3 P(2,1,1), Q(0,-3,5)

Q: Find the directions in which f increases and decreases most rapidly at point P. Then find the…

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Q: Let v = (3,4, 12) . Find the directional derivative of f(x,y, z) = x – y² +3z³ in the direction of…

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Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: NOTE:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: Find the directional derivative of the function at the point P in the direction of the point . f(x,…

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Q: Find the directional derivative of the function at point P in the direction of Q. f(x, у, z) P(2, 1,…

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Q: 1. Find the value of the directional derivative at the particular point Po for the given function in…

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Q: (3.2) The directional derivative of f(x, y) at P(1,2) in the direction of i+j is 2v2 and in the…

A: Step:-1 Directional Derivative of f at point (p, q) in the direction of unit vector say u^=u^1, u^2…

Q: Find the gradient of the function at the given point. Function g(x, y) = ye-x Vg(0, 9) = Point (0,9)…

A: Given function: g(x,y)=ye-x

Q: Find the directional derivative of f(x, y, z) = at P(4,5, –3) x + z _n the direction from P to Q(3,…

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Q: 3 Find the directional derivatives of p = 8xyz³ - 2x²y²z² at the point (2,-1,1) in the direction 21…

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Q: Find the directional derivative of f(x, y, 2) 2y at P(5, 1, –4) a + z in the direction from P to…

A: Given: fx,y,z=2yx+z, P5,1,-4, Q2,3,-1   The expression for the directional derivative of the…

Q: Find the directional derivative of f(x, y, z) = 5y at P(5, 1, –4) x + z in the direction from P to…

A: We have to find directional derivatives for the given function.

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: Q:4) Find the directional derivative of the function f(x.y,z)-x²+y*+z°-2 at the point po(1,1,1).

A: here we are not given the vector in whose direction we need to find the directional derivative so…

Q: Use Green's theorem to evaluate fxydx+ x3y3dy where C is a triangle with vertices (0,0), C (1, 0)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the gradient of the function at the given point. Function Point (8,4) f(x, y) Vf(8, 4) = = = x…

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