Math Answers

If (𝑥, 𝑦, 𝑧) =𝑋^ 2 𝑌 − 2 𝑌^ 2𝑍 ^3, find ∇𝑓 at the point (1, −1,2)

Consider the set V = R 2 . For (x1, y1),(x2, y2) ∈ R 2 and c ∈ R, define the following operations:

I. (x1, y1) + (x2, y2) = (0, y1 + y2)

II. c(x1, y1) = (0, cy1)

Is the subset a vector of R2. If not prove the axioms that makes it false.Also prove those axioms that are true.

find the value of b for which the given equation is exact, and then solve it using that value of b

(xy^(2)+bx^(2)y)dx+(x+y)x^(2)dy=0

A trapezoid has an area of 36 sq. m and an altitude of 2m. Its two bases have ratio of 4:5. Find the perimeter of the trapezoid. Find the percentage increase in the volume if its edge is increased by 1%

Find the square root of −5 − 12𝑖

Evaluate ∫f 𝑜𝑣𝑒𝑟 𝑐 where 𝑓( 𝑧 )= 𝑥^2 + 𝑖𝑦^2 where c is given by 𝑧 (𝑡 )= 𝑡^2 + 𝑖𝑡^2, 0 ≤ 𝑡 ≤ 1

Show that 𝑠𝑖𝑛𝑖𝑦 = 𝑖 𝑠𝑖𝑛hy

Using the Cauchy –Riemann equations verify the following is analytic or not

i) 𝑥^2 − 𝑦^2 + 2𝑖𝑥𝑦

ii) 𝑥^2 + 𝑦^2 − 2𝑖𝑥𝑦