The largest value of the constant b such that the vector-valued function F(t) =< cos 21It, sin (t- 1), t - 3t2 + 6 is smooth on the interval (-00, b- 2) is

Q: EX Prove that the directional derivative of f(x, y) = y² + 2xy³ + x²y² at point (0, 1) in the…

A: What is Directional Derivative: The directional derivative of a scalar function represents the rate…

Q: 4. Find the directional derivative of f in the direction of vector v at point (1,3) such that v =…

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Q: Find the point on the graph of z = 3x2 + 2y at which vector (24, 8, 2) is normal to the tangent…

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Q: 2. Find the directional derivative of o = yx2 +x²z + 3xyz in the direction of vector n = î + 2 ŷ -2·

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Q: Find the parametric equations of the tangent line to the curve represented by the vector function…

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Q: (a) (10 pts.) Consider the function h(x, y) = r³ – x sin(2y – 2) + y? Calculate the derivative of…

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Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at…

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Q: 2. Suppose that f (1,2)= 3 and that the directional derivative of fat point (1,2) in the direction…

A: Given that f1,2=3 and the directional derivative of f at point (1,2) in the direction of the vector…

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

A: The given function is fx,y=7exsiny.    point: 0,π3   and   direction vector: v=-10, 24. Obtain the…

Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter…

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Q: Show that the graph of the vector-valued function r(t) = is a circle, and find its radius and…

A: The equation of a circle is defined by the equation, (x-h)2+(y-k)2+(z-l)2=r2 , where, (h,k,l) is the…

Q: 2. Suppose that f (1,2) = 3 and that the directional derivative of ƒat point (1,2) in the direction…

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Q: 0. for the funchion f (x,4) = 3-x?- u?, find a unit tangent vector to the level curve at the point…

A: Given: fx,y=3-x2-y2-3 at P3,5​​​​​​​

Q: 3:) Consider the function g defined by g(x ,y) = cos( mxVy) + log3 (x-y) (b) calculate the…

A: Given,g(x, y)=cosπxy+1log3(x-y)To find: Instantaneous rate of change of g(x, y) at point (4,1,2) in…

Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter…

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Q: ind the directional derivative of the function f(x, y, z) = Vx² + y² + z² at point (2, -3, 6) in the…

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Q: determine where the given vector-valued functions are continuous. V(1) = (Vi-I ,,1 ). V(t): t-1

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

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Q: Compute for the directional derivative of f (x,y,z) = tan (ax – 2ny)e4y-z at the point (,0, ln 4) in…

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Q: 2. Find the equation of the normal line and the tangent to the parametric surface defined by the…

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Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

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Q: an object is moving in 3-dimensional space with velocity vector v(t)=(sin(t),t,t^2) starting at…

A: Consider the given velocity vector: vt=sint,t,t2 Find the position vector: Integrate velocity vector…

Q: 2. Prove that the directional derivative of f (x, y, z) = xy sin z at direction v = i+2j+ 2k is .…

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Q: Find the equation of the tangent line of the vector function F(t) = (e= cos(t), e=' sin(t), e') at…

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Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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

A: Given: fx,y,z=3x+7yz 1,7,-1 To find: Maximum rate of change of f at the given point. The…

Q: Given the vector valued function: T(t) = Then the point 9 units along this curve (in the direction…

A: Tangent vector two a curve always point in the direction of t increasing.

Q: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

Q: Find First and second derivatives of Funchion . tm - (e-a -a)(e-a+a) Where a is parameber

A: To find a first and second derivative by first simplify the equation and finding it's value at x=0

Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given:        fx,y,z=xy sinz         x,y,z=1,2,π2    direction v=i+2j+2k   Differentiate the…

Q: 3. Find the length of the trajectory of the vector valued function f(t) = (7V2.1,7",e-7) from 0 to…

A: The detailed solution of the problem is given in the next steps.

Q: The position vector of a particle in the xy-plane is given by for all t > 0. The acceleration…

A: position vector of a particle in the xy-plane is given by &lt; t^2+1, ln(2t+3) &gt; for all t&gt;=0

Q: Choose the direction vector for which the function f defined by f(x,v) = sin(7x)cos(13y) has the…

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Q: 5. Compute the directional derivative and gradient of f(x,y,z) = 4x – y²e3xz at (2. –1.0) in the…

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Q: An airplane took off from point (3, 0, 0) at an initial velocity, v(0)= 3j with an acceleration…

A: Let r(t) be a position vector of a particle at time t. Then the velocity vector  v(t)=ddtr(t) Also…

Q: Given the function of two variables ƒ(x, y) = 4x³ − 60x² + 12xy² − 24y² +3. - - Find and classify…

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Q: Choose the direction vector for which the function f defined by f(x, y)= sin(3x) cos(11y) has the…

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Q: The directional derivative of f(x, y) = xe + cosxy at P,(2,0) in the direction of the vector 3i - 4j…

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Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the…

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Q: Find the directional derivative of the function: f(x, y) = ez² + 4y at the point (0, 0) in the…

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Q: Find the directional derivative of the function f(x, y) = In(x +y°) at the point (2, 3) in the…

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Q: Choose the direction vector for which the function f defined by f(x, y)= sin(5x) cos(3y) has the…

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Q: Compute the directional derivative of the function f(x,y) = - xy + y at the point P(0, - 9) in the…

A: Solution-

Q: Q1. Find the directional derivative of = x²z + 2xy² + yz2 at (1, 2,-1) in the direction of vector…

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Q: Find the direotional derivative of the scalar function f-x'+ y' +2z', at the given point (1,1,2), in…

A: Explanation of the answer is as follows

Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

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Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter…

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Q: Find the derivative of the vector function ta x (b tc), where r(t) = (-1,1,-2) а %3 (-2,3, -1), ь 3…

A: Given vector function is,

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.