r) Λ (q r) Ξ (p V q) Determine whether (p r

Q: If J_f{x)dx=10 andJ, f{x)dx= 3, then J, f(4 – x)dx=?

A: According to our guidelines we are supposed to do only one question. Kindly repost the other…

Q: Find V · (V × F) if F(x, y, z) = sin xi + cos(x – 2y)j + 8zk. | V ·(V × F) :

A:

Q: Find ▼ · (V × F) if F(x, y, z) = 8 sin xi + 8 cos(8x − 9y)j + 10zk. V · (V × F) = [

A:

Q: Find V· (V × F), if F(x, y, z) = 3e**i+3xe'j – 3e²k. - V·(V × F)

A:

Q: af Find of f (4.v) = sin ) 1+ y

A:

Q: f(r,t) = cos(3r) exp(4t) %3D fi(x,t)+ frz(x,t) = f(r,t) %3D

A:

Q: (f) If F¹(x, y) = 5y sin(xy)i + 5x sin(xy)j, then f(x, y) =

A: Given vector field F→(x,y)=5ysin(xy) i→ +5xsin(xy) j→ we need to find function f(x,y) such that…

Q: Find V · (V × F) if F(x, y, z) = 7 sin xi + 10 cos(4x – 5y)j+ 5zk.

A:

Q: Find V (V x F), if F(x, y, z) = 6ei+ 9xe'j - 5e k. V. (V x F) = %3D

A: Given Fx,y,z=6exzi+9xeyj-5eyzk

Q: Find ▼ · (V × F) if F(x, y, z) = sin xi + 7 cos(9x - 10y)j + 5zk.

A:

Q: Find V · (V × F), if F(x, y, z) = 5e²i+ 5xe®j– 7ev²k. %3D V ·(V × F) =

A: We know divergence of curl of any vector v is always zero.

Q: Q2: Expand f(x, y) = [sin (x y³)]? about , 1). Q3: Given T(u) = sin (u), where u = /x2 + y?, find…

A: Concept: " since you have asked multiple question, as per our guidelines we are supposed to solve…

Q: Find V · (V × F) if F(x, y, z) = 6 sin xi + 6 cos(6x – 7y)j+ 2zk. | V· (V × F) =

A:

Q: 17 and g(x) = 'Vx, find (f o g)(x) and (g o f)(x). Then determine wh %3D fo g)(x)?

A:

Q: FI = r Where f(r) = -i = 2xi – 3yj + zk So be it %3D div) grad(f) find

A:

Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 7 cos(9x – 10y)j + 3zk. V·(V × F)

A:

Q: (f) f(x1,x2) = xî xª, where 0 < a<1, on R?+.

A:

Q: F(t, x, y, 2) = [0, cos(t), sin(t)] x 7, 0<t<

A: Solution

Q: Find V· (V × F), if F(x, y, z) = e*²i+3xe'j – 7e*k. V . (V × F) = x z evz 三

A:

Q: Find V· (V × F) if F(x, y, z) = 7 sin xi + 5 cos(7:x – 8y)j + 6zk. V . (V × F) :

A: F(x,y,z)=7sinx i+ 5 cos( 7x-8y)j+6zk

Q: f(x, y) %3D 3ху + у? (а) f(x + Дх, у) f(x, у + Ду) — f(x, у) - (b) Ду Зх + 2y + Ду Ду # 0

A:

Q: a) f(x,y) = xcos(V) + ye*

A: We apply first and second derivative over function

Q: f(z) = 3z° cos(z) f'(z) =

A: To find f'(x)

Q: Find V · (V × F) if F(x, y, z) = 3 sin xi + 6 cos(6x – 7y)j + 3zk.

A:

Q: Find V · (V × F), if F(x, y, z) = e"i+ 3ze'j – 5e"k. V. (V × F) =

A:

Q: f (r, y) = x² (x, y) = x´- e sin y (0 < y ST

A: Given f(x,y)=x2-xsiny. We need to find the extrema if exists.

Q: Given that f(z) = y – x – 3x²i. Find S f(z)dz OB B-1+i A=i

A:

Q: f(x, y) = iy² – x², P(1,4), v = 2i + j

A:

Q: Q/ Let X be the r.v such that E(X) = 2, E(X²)= 2a , E((2+aX)²) = 2a3 Find the value of a. %3D %3D

A: Let X be the random variable such that, E(X)=2, E(X2)=2a, E((2+aX)2)=2a3

Q: س/ أختار قيمة R ,D المناسبة ل لداله الاتية f(x) = 2 + Vx? - 1 Df = {x:xeR:x 0} O الخيار رقم 1 D, =…

A: The given function is fx=2+x2-1. Calculate the domain and range. Range is defined the all possible…

Q: dz where a inside r= C z-a 2ni

A: We have to find integration of given function Using Cauchy's Integral Formula.

Q: f z = f (x, y), where x = r cos 0 and y = r sin 0, show that a2 z 1 a²z 1 dz ar2 ar2 p2 aA2 r ar

A:

Q: Find V· (V × F) if F(x, y, z) = 4 sin ci + 7 cos(9x – 10y)j + 10zk. V · (V × F) =

A: Given F(x,y,z)=4sinx i+7cos(9x-10y) j+10z kTo find∇·(∇×F) first we need to find ∇×Fwe know that ∇×F…

Q: Find f. f '(t) = 2 cos t + sec?t, , -1/2 < t < «/2, _f(x/3) = 3 f(t) =

A: Given: The derivative function f'(t)=2cost+sec2t , -π2&lt;t&lt;π2 , fπ3=3. To find :  The function…

Q: Find V. (V x F), if F(x, y, z) = 6e"²i+ 3xe"j – 6e²k. - V· (V × F) %3D

A:

Q: Find V· (V × F) if F(x,y, z) = 7 sin xi + 9 cos(6x – 7y)j+ 6zk. V·(V × F)

A: The solution is given as

Q: Find . for (x,y) = x² + y² af af ду' дх Find ду' дх Je Je for f(x,y) : sin xy? x2+1

A:

Q: f f Find Af = where f(r, y) = In (9r2 + 5y2 – 3r). %3D

A: Here f is two variable function .To find ∆f , first calculate fxx and fyy then add them.To find fxx…

Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 5 cos(8x – 9y)j+ 4zk. V· (V × F)

A:

Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = 2 ¿i + k - Duf i

A: Given that       f(x,y,z) = 6x5y3z4 ; P(1,-2,1); u=(1/3)I+(2/3)j-(2/3)k  Here we have to find Duf at…

Q: Find V · (V × F), if F(x, y, z) = e2²i+ 7xe'j – 2e²k. - V·(V × F) =

A: Solved below

Q: Find V. (V × F) if F(x, y, z) = sin xi + 8 cos(10x – 11y)j+ 3zk. %3D - V·(V × F) :

A:

Q: sin(r. r dr dy. Compute O y/3

A: To evaluate∫01∫y131sin(πx2)x2 dx dyx= y13y = x3

Q: Find V (F x G), if F(r, y, z) G(x, y, z) = xi+ yj - zk. = 2xi +j+ 8yk and V. (F x G) =

A:

Q: Find (∂ w/∂ x)y, z if w = x2 + y - z + sin t and x + y = t.

A: To find the partial derivatives.

Q: Find V· (V × F), if F(x, y, z) = 7e*²i+ 6xe"j –- 6e²k. V·(V × F)

A:

Q: 16. f(x, y, 2) = y - Vr? + z?; P(-3, 1, 4); a 2i-2j-k

A: To find the directional derivative of f at P in teh direction of a So, given f(x,y,z)=y-√(x²+z²);…

Q: If f(2) = sin(z?) = U(x, y) + iV (x, y), determine U and V. Verify that the C-R

A:

Q: Find V· (V × F), if F(x, y, z) = e®²i+ 4xe®j – 5eV²k. V.(V × F) =

A:

Q: Find V. (V x F) if F(x, y, z) = 4 sin xi + 7 cos(8x – 9y)j+ 9zk. V·(V × F)

A: