this curve,
with X - axis rotation, calculate surfacea area
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this curve, with X - axis rotation, calculate surfacea area y=e-72, (x > 0)
Evaluate the following integrals. (a) / In(3x) dx for x > 0 (e) / ( +er) dx (n lete* dx (e) sin(5x +1) dx
check if e-1/4/ f(x) if x > 0 if x < 0 is differentiable at 0.
Problem 2. Let f be a self-map on a set X. For x,y e X define x ~ y if and only if f"(x) = f(y) for some integers n, m > 0. Show that ~ is an equivalence relation.
Determine the moment of inertia of the shaded area about the x axis and the y axis. Figure < 1 of 1 > 1 m
Find the area of the surface obtained by rotating the given curve about the x-axis. x = 20 cos (0), y = 20 sinº (0), 0 <O< 2 Preview
With double integral find surface area when y=e", y = x, y = 4 and axis y with y <et
Use induction to prove that 0–0 4j3 = n4 + 2n3 + n2 where n > 0.
Assume that X and Y are independent and follow normal distributions with Hx (a) evaluate P(X +Y > 24) (2pt) (b) that P(z < X-Y < 10) = 0.2 (3pt) find r such
. For > 0 and A > 0, define the joint pdf -Ay = 0<x<A,<y, fx.y(,y) 10 else. (a) Express c in terms of X and A. (b) Find E[XY]. (c) Let [2] be the largest integer less than or equal to z. For example, (3.2] = 3 and [2] = 2. Find the probability that [Y] is even, given that 4 <x< 34
Let f(x, y) 2e-(x+y), x > 0, y > 0. Show that X, Y are independent. What are the marginal PDFS of each?