3. Compute V×F, where: F = 2xzi + 2yz?j+(x² + 2y²z – 1)k; а. b. F = axi + byj + czk; xi+yj F x2+y2' с. d. F = yi + zj +xk; F = - i Vx²+y2 j+ Vx2 + y?k е. 1:0.

Q: Show that (2o + h)" – 2ö = nz- | n-1 lim h→0 h for any zo E C.

A: To show: limh→0z0+hn-z0nh=nz0n-1for any z0∈ℂ

Q: 9. Determine whether each of these functions from R to R is a bijection. а. f(x) %3D 2х + 4 b. f(x)…

A: Question 9) (d) We have to determine whether the following function from R to R is a bijection or…

Q: The dot product of two vectors can be written in the form x = 00 s+ X1 X2 and y = in R" is defined…

A:

Q: Some body started at A(6, 0) and coordinate change by AX = -6 and AY : O Find its new position ? *…

A: We find coordinate of new position

Q: O 2 2] B = 0 2 0 0 0 2 TRUE or FALSE: B is diagonalizable.

A:

Q: F(x, y, z) = (z sint z sin(ar), e²y-2 X b+y

A:

Q: V7x+2-V6x+4 = )f(x مستمرة عند 2 = ۲ if x 2 and x # 2 1- قيمة الثابت الذي يجعل الداله (x-2) if x = 2

A: Continuous at x=2,  using rationalization

Q: Assume that u. v = 6, ||u|| = 8, and ||v|| = 5. Calculate the value of (9u + v) · (u — 3v). (Give…

A:

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Differentiate: 3 a) F(y) = ( (y + 5y³) x²e* b) f (x) : x2+ex А c) f (x) : B+Cex

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: Obtain the GS of: 2 (Згу — 4у + 6) dz + (23 — ва? ? — 1) dy %3D 0 - a. x³y – 2x?y3 + 3x² b. x3у —…

A:

Q: Use the equations OF JF дг дх Əz ду and дх OF ду OF dz Əz Əz მz to find and дх ду ez = 6xyz II || მz…

A: ​∂x∂z​=ez−6xy6yz​∂y∂z​=e2−6xy6xz​​Explanation:Step 1:​Given an implicit function.ez=6xyzTo find: The…

Q: Find dz (3z4+4) 1 3a1-72+4 Option A Option B 36a° /E(3a1+4) (3r-4)* 3a -6r+4 -69r+4 VF(324+4) Option…

A:

Q: Зт m m 2 (т - 3)x? +. 4 -5 = - 4myx т - - Y- 4

A:

Q: Evaluate v (x? v + x y z²) · dr where C is the line segment from (1, – 1,0) to (2,1,3) | Select one:…

A:

Q: TEST FOR HOMOGENEITY: 4. e √x x-2xy x - y

A: A function f(x, y) is said to be homogeneous if f(Kx, Ky) = Knf(x, y)  where n is any real number…

Q: Verify that 5 18 11 2²4 ахду 22+ дуох - for f(x, y) = 2x³y6 - 4x5y4.

A:

Q: Using the substitution u = (A) (B) C D 1+1 du [₁ -1/2 du [(u ¹/2 - u-1/2) d du (u - 1) / u-²1) x + 1…

A:

Q: 3.a) Eliminate the Arbitrary Constants in the equation: y = C1sin(2x + C2) y" + 4y = 0 у' — 4у%3D0 O…

A:

Q: For nos. 1 and 2, use separation of variables to find a product solution to the following: ди ди 1.…

A:

Q: Determine the vesulting equaton Determine the vesulting equaton after using the suitable…

A: We have to find

Q: Solve for w where u = (1, -1, 1, 0) and v (2, 0, –1, 3). 3w = u - 2v w =

A:

Q: 2. อใน at2 a อริน 0x2

A:

Q: Write the following equation in the form w = u(x,y) + iv(x,y) h(z) = (3z + 2i) / (2z2 + 4)

A:

Q: Q) Verify that (bx с) %3D b.(с х а) — с. (а x b) if a %34i — 3ј +6k , b- 5i +4j — 3k, с %3 4i +6j +3…

A: Given the three vectors

Q: Let Z₁ = a 2 i Z₂ = 3 - 2 i If Z₁ x Z₂ = 8 - 14 i, calculate a:

A: