11.7 Let HG and K◄ G, and assume that HNK={e}. Show that if x € Hand y EK then xy =yx.

Q: 20) Given that y varies inversely with x, when x = 12, y = -2. Find k and then find y when x 3. k =…

A: Given : y varies inversely with x When x=12 then y=-2

Q: 10 Sx³ex¹⁰dx= (Type an exact answer.)

A: Given integral is as follows

Q: Prove that CL dx = ln lx1+C. Chint): set x

A: Please refer to the image below.

Q: 3. If EEP'S FERY zooming in toward the point (1, 1) on f(x, y) = x(x² + y2)-3/2 sin(x²y) find f.(1,…

A:

Q: FL Let b > 0, b 1. Which of the following must be true if y = Check all that apply. hip O = b* In(b)…

A: no need of explanation as it is itself a formula

Q: Let v = [1] and let z = [¹] x The Projx is equal to k k [21] where

A: Our objective is given below:

Q: Ex2:] If S:= {1/n - 1/m:n, mEN3, find inf Sand sup S.

A:

Q: B. Let H « G and K - G, and assume that HNK = {e}. Show that if x E H and y E K, then xy = yx

A: We can prove given result by definition of normal subgroup:

Q: Given that In2 = v and ln3 = w, express each ofthe following in terms of v and w. a) ln 576 b)…

A:

Q: II. Evaluate the following. 1. z = ji

A: Given: z=jj

Q: Show that if a, = (a" – B"), where a = (1 + v5)/2 and ß = (1 – V5)/2 , then th An = an-1 + an-2 and…

A:

Q: If z is implicitly defined as a function of x and y via the equation e² = xyz, compute 33 and 3.

A: The given equation is, ez=xyz. To find: ∂z∂x,∂z∂y. To compute ∂z∂x,∂z∂y : Partially differentiate…

Q: a = 268 b = 752 e. Prove that if g = gcd(a, b) then gcd (2) = = 1

A: Given that a = 268 = 2 × 2 × 67 b = 752 = 2 × 2 × 2 × 2 × 47   Now let g = gcd (a, b) = gcd ( 268,…

Q: Let X B(25,0.2). E(X²) = Select one: O a. 41 Оъ. 29 О с. 25 O d. 0

A:

Q: 8. Approximate 3.9996 using linearization.

A: