Question: Consider the following equation. f (x, y) = y4/x, P (1, 3), u = 1/3 (2i+sqrt (5)j) (a) Find the gradient of f. ?f (x, y) = (b) Evaluate the gradient at the point P. ?f (1, 3) = (c) Find the rate of change of f at P in the direction of the vector u.

Answer to Consider the following differential equation. (x − y4

Let Y1 < Y2 < Y3 < Y4 < Y5 be the order statistics of five independent observations from an exponential distribution with pdf f (x) = e −x for 0 < x < ∞. (1) Find the pdf of the sample median Y3.

Let Y1 < Y2 < Y3 < Y4 < Y5 be the order statistics of five independent observations from an exponential distribution that has a mean of θ = 3. (a) Find the pdf of Y1 (b) Find the pdf of Y5 (c) Find the pdf of the sample median Y3.

Let Yi < Y2 < Y3 < Y4 < Y5 be the order statistics of five independent observations from an exponential distribution that has a mean of = 3. • Find the pdf of the sample median Y3.

Let Y1 < Y2 < Y3 < Y4 < Y5 denote the order statistics of a random sample of size 5 from a distribution having pdf f (x) = e-*, 0 < x < oo, zero elsewhere. Show that Z1 = Y2 and Z2 = Y4 - Y2 are independent.

Question: If f (x,y)=xy2x2+y4, does lim (x,y)→ (0,0)f (x,y) exist?Hint: Find lim (x,y)→ (0,0)f (x,y) as (x,y)→ (0,0) along the line y=x and along theparabola x=y2.

Engineering Electrical Engineering Electrical Engineering questions and answers Given vectors A = x + y^2 - z3, B - x2 - y4. ami C = y^2 - z4, find A and a. the component of B along C theta_AC, A times C, A middot (B times C). A times (B times C). x times B. and (A times y) middot z.

EXAMPLE 3 If f (x, y) = - (x,) =av21 A does l im f (x,y) exist? SOLUTION Let's try to save some time by letting (x,y) → (0,0) along any nonvertical line through the origin. Then y = mx, where m is the slope, and f (x, y) = f (x, mx) = 7x ( mx )? 8x2 + (mx) 7m2x3 - 7mx 8x2 + m4x4 8 + m4x2 as (x,y) → (0,0) along y = mx. So f (x,y) → Thus f has the same limiting value along every ...

Let Yi < Y2 < Y3 〈 Y4 〈 Y5 〈 Y, be the order statistics of a random sample of size n = 6 from a distri- bution of the continuous type having (100p)th percentile Tp.