If ø(x, y, z) = ry²z find grad ø at (2, – 1, 3).
Q: If C is the line segment from (6, 1) to, (0,0), find the value of the line integral: S(5y i+ x) • dr…
A:
Q: ®. *,(t)=l, tilt)=t, Xglt) =t² Let [oD. Use Gran-Schridlt on er thogonolize e, 2) process to
A:
Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…
A:
Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…
A:
Q: 8.If V=k r°, and V=4 when r=2 if dr/dt =2, find dV/dt ind th
A:
Q: Suppose that over a certain region of space the electrical potential V is given by the following…
A: Given data: The expression for the given electrical potential function is: V(x,y,z)=3x2-2xy+xyz.…
Q: Let f(x, y) = xcosy- y'e*y. fry at (1,0)is equal to: %3D | -2/3 -2 1
A:
Q: Given a level suface 4x2y2 + 5xy = 4 with y = y(x). Find! dy at the point (3, 2). Give your answer…
A: A detailed solution is given below
Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (d) z = sin (4x + 5y); x = s + t, y = s - t
A: Given that, z=sin4x+5y ; x=s+t ; y=s-t Then we get, z=sin4s+t+5s-t⇒z=sin4s+4t+5s-5t⇒z=sin9s-t
Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D
A:
Q: In(u cos v) and y = usin v. Evaluate and z at the point 2е" In y, x 3D (u, v) = (2, 7/4). Let z = du…
A:
Q: pプ PG2-2(6x)さ子エ theorem over the elosed hemispher defined bY Zz J25-x²_y?
A: Given that F→=x2+yi^-zyj^+z2k^ and z=25-x2-y2
Q: Given z = 17 In(t) and y = 289 t then fir dy d'y dx?
A: Differentiate given function
Q: If x2 + y? + z2 = 9, dt dy = 9, find dt dz when (x, y, z) = (2, 2, 1). = 4, and %3D dt %3D
A:
Q: Given z = 18 In(t) and y = 324 t2 then find dy dz dy da?
A:
Q: if x²+y²=t-- and x*+y*=t*+=,prove dy X t dx 3. ху
A:
Q: Obtain ∫C ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π
A:
Q: Let ry w = and a = 2s + t, y = st, z = 2s - t dw dw Find ds' at
A:
Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…
A:
Q: The line integral 2xe" dæ + a²e" dy + (1 – 2²)e¬²² dz is not independent of path.
A: The line integral ∫CF·dr is independent of path if the curl of F is zero, that is, ∇×F=0. Here, The…
Q: If C is the line segment from (1,3) to, (0, 0), find the value of the line integral: S(3y² i +3x}) ·…
A:
Q: Consider h(x,y, z) = cos (xy) + eY² + In (xz) at the point P ( 1,0, = 1 Deter-
A:
Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to: %3D 1
A:
Q: # 4. Evaluate the line integral | (x +2x²y) ds, where C is the upper half of the unit circle x2 + y2…
A:
Q: If V=3x^2i+4y j+k_andl=ri+t^2.j+t^3 k.FindS V. dl wherea=(0,0,0) and b = (1,1,1).
A: I = xi + yj+ zk
Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition
A:
Q: Wyx %3D If w = e* + x In y + y In x prove that Wgy
A: Consider a multivariable function . Then the derivative of the function with respect to x is the…
Q: 0 0 0
A:
Q: Given z=200st+17 and y=9sint dr dt dy dt dy da %3D
A: First of all we will differentiate the given equations with respect to t
Q: Given z = 15 In(t) and y =225 t then find dy da dy da?
A:
Q: 27. Consider the piecewise path which goes along (t,3 – 3t, -t) for 0 <t<1, then along (1,t,-1+ t)…
A: Line Integral along the given parametric curve.
Q: If w= 2e*_lnx find dw/dt , x=In(t^2 +1), y=tan t, z=e^t
A: If w= 2ex lnx Find dw/dt, x=ln(t2+1) dw / dt = [ ∂w/∂x ] [ dx/dt] + [ ∂w/∂y ] [ dy/dt]…
Q: If W = xyz with x = 2t*, y = 3t-, and z = 4t¬³, what is dw dt 24 O In(t)
A:
Q: Given z=3 In(t) and y=9t² then find dy de dy da %3D
A: We use parametric differentiation
Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).
A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…
Q: Use Green's theorem to evaluate s cy? oy)dx + (y²rlo4") dy where Cis s hoon belbw, N y = 2-x² G,1)
A: The given path contains 4 curves: C1: from (1, 1) to (-1, 1)C2: from (-1, 1) to (-1, -2)C3:…
Q: dw If w = f(x, y, z) = In(x² + y? z?),x = cost y = sin t ,z = 4VE , then is : dt %3D %3D
A:
Q: If u=lx+my and v=mx-ly,show that 1? + m? ди ди 1 + m?
A: Given u = lx + my v = mx - ly
Q: Given z 15 In(t) and y= 225 t then find dy da dy dr?
A: Given that: x=15ln ty=225 t2
Q: Given: ARST = AXYZ; SK bisects ZRST; K YL bisects 2XYZ. Prove: SK = YL S
A: Prove SK≅YL.
Q: 16. WXYZ is an isosceles trapezold with WX ZY If mĐW = (2x)° and mĐZ = (x +27)°, find the value of…
A: We have to find x
Q: IF V= xe+ y2+z*.express in itr rimplert porm dy
A: Topic = Partial derivative ∂V∂x⇒Differentiate V w.r.t 'x' take constant y and z.∂V∂y⇒Differentiate…
Q: Findd Fhie boundled by Ahe Cureo area 2. X= 3J-y' and x+Y=3 ーレ
A:
Q: Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following…
A: To determine the rate at which the box’s (a) Volume, (b) Surface area and (c) diagonal length are…
Q: ) Find dw if w = xe³/², x = t², y = 1 — t, and z = dt 1 + 2t.
A: Topic:- application of derivatives
Q: If y= V (x-1), find dy (Use rules, not a de finition ) Xp
A:
Q: If z'y +y = r dy 1, then at (0,-1) is
A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…
Q: Evaluate ∮C(yexy−sinx)dx+ (xexy+ 1)dy where C is the path r(t) given by x=t,y=π/2(t−1)2 from t= 0 to…
A:
Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…
A: Given that dydt=yβ-αy and y=y0 at t=0 We have to find the solution of the above equation.
Step by step
Solved in 2 steps with 2 images
- 30. If E 200 cosh 2x sin 2y a,+ 200 sinh 2x cos 2y a, V/m, find the equation of the di- rection line passing through the point P(1,0,0) and sketch it in the z-0 plane for 0 < x < 5 and 0 < y < /4.Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).Find ∂w∂s and ∂w∂t when s = 1 and t = 2π for w = xy + yz + xz where x = s cos t, y = s sin t, and z = t.
- Find the value of ds / du at u = 2 if s = t2 + 5t andt = (u2 + 2u)1/3.Use Euler’s Method with h = 0.1 to approximate y for t = 0.1, 0.2, and 0.3.Suppose that the position of one particle at time t is given by x1 = 5 sin(t), y1 = 2 cos(t), 0 ≤ t ≤ 2? and the position of a second particle is given by x2 = −5 + cos(t), y2 = 1 + sin(t), 0 ≤ t ≤ 2?. 1) find the collision points. (Enter your answers as a comma-separated list of ordered pairs. If an answer does not exist, enter DNE.)
- Consider h(x, y, z) = cos (xy) + e^yz + ln (xz) at the point P (1, 0, 1/2). Determine the following:Suppose w=x/y+y/z, where x=e^(4t), y=2+sin(4t), and z=2+cos(3t). A ) Use the chain rule to find dw/dt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e^(4t) as x. dw/dt=? B ) Use part A to evaluate dw/dt when t=0.A particle moves in the xy-plane in such a way that its path is defined by x = e^t cos t and y = e^t sin 2t. Find the speed of the particle when t = /2.
- Find the value of dw / ds at s = 0 if w = sin (e√r) and r = 3sin (s + π/6).Suppose w=x/y+y/z, wherex=e3t, y=2+sin(t)x=e3t, and z=2+cos(6t). A ) Use the chain rule to find dwdtdwdt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e3t as x. dw/dt= B ) Use part A to evaluate dwdtdwdt when t=0.Suppose z=(x^2*sin(y)), x=(5s^2−3t^2), y=(−2s*t)