By about how much will f(x,y,z) = In Vx +y +z change if the point P(x,y,z) moves from Po(6,2,6) a distance of ds 0.1 unit in the direction of 3i 6j - 2k? The change in value is about df (Round to four decimal places.)

Q: Consider the curve defined by y = 12 1 from I| 16x6 x = 2 to x = 4. 4 The length of this curve is L…

A:

Q: The velocity of the body is given by: v(t) = 2t, 1≤t≤5 = 5t² + 3, 5<t≤ 14 where t is given in…

A: Given : vt =2t , 1≤t≤5       =5t2+3  ,5&lt;t≤14 Find : a. Trapezoidal Rule where n=2          : b…

Q: curve is 42 br then a= ? If the length of the 0 <x< a apart of the y =x³/2 16 - O A) 17 O B) 3 О С)…

A: we have the length of the curve . We have to find the value of a

Q: 18. The length of the curve y = r* from r = 0 to r = 2 is | V1+2® VItz® dz B. | V1+3x2 dx A. C. D.…

A: Question 18 is solved. Solving more questions are against the policy of bartalby. In question 18 ,…

Q: The linear approximation for f(x,y)=Vy+cos?(x) at (0,63) is O L(x.y)=(65+y) 16 L(x,V)=(65-y)

A:

Q: • The derivative of f(x, y) at a point P is greatest in the direction of i = 2i + 2j – 2k. In this…

A: Given that derivative of f(x, y) at point P is greatest in the direction of In this direction, the…

Q: d the directional derivative of V = r²z sin o along the direction A = 3r - 22 N evaluate at…

A: Given, V=r2zsinϕA→=3r→-2z→

Q: Q6 - Tf the position vecter of aPartick P is Vt) = <3 Cost.5 Sin t.4 Costy 1- Show the Speed of the…

A: Given that, r(t)=&lt;3cos(t),5sin(t),4cos(t)&gt;

Q: 5. T'he surface of a pice of bubble wrap is given by the function f(r, y) = cos(r) sin(3). In which…

A: Given: The surface of the bubble wrap:fx,y = cosxsiny--------------------------------To find: The…

Q: F(x, y) = 9xy2 i + 9x²y j C: r(t) = (t + sinnt), e + cos(÷nt)), osts 1 (). (a) Find a function f…

A:

Q: pY (y | 0) = 0"(1 – 0)'-", y = 0 or 1, where 0 < 0 < 1 is a parameter. a) Find an estimator ÔMOM of…

A: In method of moments, the theoretical moments are equated with the sample moments in order to…

Q: - A tank contains 120 liters of oil initially. Oil is being pumped out of the tank at a rate R(t),…

A: A tank contains 120 litres of oil initially. Oil is being pumped out of the tank at a rate R(t),…

Q: Let f (z)=7. Find f (z )dz from z =0 to z =4+2i along the curve C given by z =t? +it. (A) –10 – (C)…

A:

Q: 1. Evaluate z dz, where the contour C goes from z = 0 to z = 1 to z = 1+i.

A:

Q: c0.5 x In(r + 1)dr. Use the Midpoint Rule with n +2 = 8, to approximate J-0.5 Area 2

A: Solution:GivenTo approximate     ∫-0.50.5x ln(x+1)dxwith n+2=8Formula:Area=∑i=1nfxi-1-xi2∆x

Q: b. Given the equation of the curve x =f(y) is x = Jy+1 and 2 fy)dy k = h suggest a value for h,…

A: Given - there are two Cup C and Cup D represent solids of revolution.             The cups have…

Q: 20. The curve 2x2y+ y 8x +1 passes through (4, 1). Using the tangent line to the curve at the point…

A:

Q: b) Find [[F.dS, where S is the top and the side (but not the bottom) surface of the cylinder r + y <…

A:

Q: The tangent plane to z = f(x, y) at the point (1, 2) is z = 3x + 2y – 5. (a) Find f,(1,2) and f,(1,…

A:

Q: A particle moves on a coordi-nate line with acceleration a = d2s/dt2 = 15sqrt(t) - (3/sqrt(t)),…

A: Given:

Q: Q.2) Find the orthogonal trajectories of the family of curves e*(x sin y– y cos y) = c

A: 2 Given family of curves is e−xxsiny−ycosy=c. We have to find the orthogonal trajectories of the…

Q: Q: Find the condition that the line x cos a +y sin a = p may touch the curve x"y" = a™*".

A: Answer

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 5t…

A:

Q: dA When the radius r of a sphere increases with time t, the change in area is dt O a. dr 4a r dt O…

A: Surface Area of sphere = 4πr2  r= radius of sphere

Q: The derivative of f(x, y) = e* sin y in the direction of 0 is given by cos y-V3 sin y Du f(x, y) =…

A:

Q: Find the work done by F=xy³i+ 4x2y2j in moving a particle once counterclockwise around the curve C:…

A: We have to find the amount of work done.

Q: 1. Sketch in the xy - plane the domain of each function : (a) ƒ (x, y) = (Vx – 1+ Vy +1) · In (x² +…

A:

Q: The curves C,: x=t, y=ť, z=t°, t20 and C,: x= sint, y = 1+cost, z= 1, t20 have intersection at the…

A:

Q: az a) If z= zy – Te. , show that z = ry+z. b) The surface area S of a right circular cone of radius…

A:

Q: Find the length of the curve F(t) = (4 cos(3t), 4sin(3t), 3t) for -8<t< 10 Give your answer to two…

A:

Q: By about how much will f(x.y.z) = In /x +y +z change if the point P(x.y.z) moves from Po(6,1,3) a…

A:

Q: Find the rate of change f(x, y) = In(6x? + 10y?) at (V2, v2) in the direction making a (positive)…

A:

Q: A partide moves along the x-axiİS, The velocity of the particle at time t is ot-t.A gřaph is given…

A: Given, The velocity of the particle at time t is vt=6t-t2

Q: 1. Consider the function f(r, y) = 70 – 4.x2 – y2. (a) Find the tangent plane to f(x, y) at (-3,…

A:

Q: - A duck is flying the helical path r cos(t), y = sin(t), and z = t with t in seconds. TE emperature…

A:

Q: A particle moves in the xy plane so that at any time –2 <t< 2, x = 3 sin t and y =t – 4 cost + 1.…

A:

Q: The derivative of f(x, y, z) at a point P is greatest in the direction of i = i + 2j+ 2k. In this…

A:

Q: mos t Y Using accurate centered li ff. fommula approximate error in and then słate the approxi mahin…

A: Please check step 2 for the solution.

Q: The tangent to the curve x? – xy + 2y? – 4x + 2y +2 = 0 that is parallel to the line x– 4y = 2. The…

A:

Q: 3) dilation of 1.5 about the origin 4) dilation of 2 about the origin Ay A y K M 6) dilation of 1.5…

A:

Q: 3 For which values of a E R the tangent plane to the graph of f(x, y) = 1+ sin(ax + y²) at the point…

A:

Q: -32 ft/sec?. Assume that the in n object's downward acceleration is given by y"(t) = elocity is y'…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: A curve joining the points Pi and P2 in R2 is parameterized by two different paths, 7(t); t1 0.…

A: Given: →γ(t);t1≤t≤t2→(τ);τ1≤τ≤τ2β To find: a) Prove that ∫t1t2→γ'(t)dt=∫τ1τ2→β'(τ)dτ. b)…

Q: An ant is crawling along the floor along a predetermined path. At time, t, the (z, y) position of…

A: Given xt,yt=1-t2,t2-6ta. ant's position at time t=0put t=0 in the above function we…

Q: Evaluate fy and f, at the given point. f(x, y) = e³Y sin(x), (T, 0) fx(T, 0) fy(T, 0) %3D

A:

Q: 1. The density of a rectangular plate at the point (x, y) is given by f(x, y) grams per cm², where x…

A: GIVEN: The density of a rectangular plate at the point (x, y) is given by f(x, y) grams per cm3,…

Q: Over a certain spatial region, suppose that the temperature T is given by T(x,y, z) = 5x2 - 3ry+ xyz…

A: We are given that the temperature T is given by T(x, y, z)=5x2-3xy+xyz. Further, we assume that a…

Q: When mineral deposits form a uniform coating 1 mm thick on the inside of a pipe of radius r (in mm),…

A: We have to sketch  f(r) = π r2 - 2r + 1.