A particle moves along a line with velocity function v(t) = t2 – t, where v is measured in meters per second. (a) Find the displacement during the time interval [2,5] (b) Find the acceleration after 2 seconds.

Q: 2. Find the derivative of the function at PO in the direction of u. f(x,y)=6x-7y, P0(-7,-2), u=4i-3j

A: We have to find derivative

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Q: Allow f(x, y) = xe^(xy), now find the maximum rate of change of f at the point (3, -1).

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Q: Find the maximum rate of change of f(x,y)= e^x^2 at (3,0) and the direction in which it occurs.

A: GIVEN DATA : Function fx,y=ex2        TO FIND : Maximum rate of change at 3,0 and the direction  The…

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Q: Find the maximum rate of change of the function f(x, y) : 4y4 at the point (1,3)

A: We will solve the problem

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the maximum rate of change of f(x,y) =x²y+ /y at the point (1,1). In what direction does it…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The maximum value of a function f occurs in the direction of the gradient of the function f and this…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. Зx +…

A:

Q: (d) Find the directional derivative of f(x, y) = x²e¬y at (-2,0) in the direction towards the point…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given that: fx,y=2sinxy,               0  ,  5

Q: (a) Find the derivative of fix. y. 2) = x-xy-z at P1, 1,0) in the direction of v = 2i- 3j + 6k. (b)…

A: The directional derivative of a function f(x,y,z) at the point (x,y,z) in the direction of vector v…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, y)…

A: Given:        fx,y=4yx   at point 4,5     The rate of change of f is     ∇fx,y=∂f∂x,∂f∂y…

Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

A:

Q: Find the direction in which f (x, y, z) = z e*Y increases most rapidly at the point (0, 1, 2). What…

A: Given Data: Function: fx, y, z=zexy Point: x, y, z=0, 1, 2   The gradient of the function is, ∇fx,…

Q: A particle moves on a straight line with velocity function  v(t) = sin(ωt) cos2(ωt).  Find its…

A: The given velocity function is,

Q: (a) Find the derivative of ƒ(x, y, z) = x3 - xy2 - z at P0(1, 1, 0) in the direction of v = 2i - 3j…

A: We have given function fx,y,z=x3-xy2-z, point P01,1,0 and vector v=2i^-3j^+6k^

Q: Find the derivative of the function at Po in the direction of A g(x, y) = x - (y/x) + V3 sec (2ry),…

A: Let us consider the given function z=f(x,y) The directional derivative of the function at Point P in…

Q: Find the derivative of the function f(x,y,z) = x² + 2y? – 3z2 at the point v =. Po = (1,1,1) in the…

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Q: Find in what directions does flx, y, z) = 4x 2– 9z + 2z In(y) increase and decrease most rapidly at…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs…

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: True or False The velocity of a particle whose position at time t is s(t) is the derivative s′(t).

A: Our Aim is to tell whether the statement the velocity of a particle whoseposition at time t is s(t)…

Q: Use differentiation to find the gradient of the curve y : = ax sin(bx) at x = 3.

A: The solution is given as

Q: Find the maximum rate of change of f(a, y, z) tan(6z + 4y + 2z) at the point (- 4, 3, - 6).

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The given function is: f(x,y)=8yx

Q: Find the derivative of the function at Po in the direction of u. 3x f(x, y) = tan -1 , P0(-2, 3), u…

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Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: According to the given information, it is required to find the maximum rate of change of f at the…

Q: Find the magnitude of the greatest rate of change of f(x, y, z) = (x2 + z2)3 at (1, 3, -2), and…

A: Consider the provided question,

Q: Find the directional derivative of the function f(x, y) = x² + y³ at the point (2, 1) in the…

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Q: 2. Find the derivative of f(x, y, z) = x³ - xy2 - z at Po(1,1,0) in the direction of V = 2ỉ – 3j +…

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Q: Find the maximum value of the directional derivative of the function f(x, y) = tan at the point…

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Q: Find the maximum rate of change of the function f(x, y) 3y5 x at the point (3,4)

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Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x - (y/x) + V3 sec-…

A: Given problem:-

Q: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)?

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given that: f(x,y)=8sin(xy),    at (0,4)

Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 3z) at the point (– 2, – 3, – 6). - -

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: We have to solve

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the maximum rate of change of f(x, y) : = ye* at the point (0, 2).

A: Introduction: Let f(x,y) is the function of two variables x and y. then the maximum rate of change…

Q: Find the maximum rate of change of f(x, y, z) = tan(7x + 3y + 6z) at the point (4, – 5, 2).

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Q: -2 In(x) Consider the function f(x, y) = 3y

A: We have to find the derivative of the function f(x,y) in the direction u=-5,2.…

Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at…

A: Note: The directional derivative of a function is the rate at which the function changes at a…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.