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: 2. Determine the power set p(A) = {{a, b}, {c}, {d, e, f}} 3. Suppose A = [7, e,0} and B = (0,1}.…

A:

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

A: Given integral is as follows

Q: 1. (e)dydx

A: Now we will solve the integral using substitution form.

Q: Find the values of (A² E¯') u̟ and (A² u,)(E-u). Are they equal.

A:

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,…

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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: Ive for æ if In(x? – 1) = 0.

A:

Q: 3. If Ax) = , find f"(-1). c. 0 d. -1 a. e b. 2e

A:

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: TOPIC: SETS 1. List the elements in the set. (x x < 3and xe Z) 2. List the elements in the set. (x 2…

A: To list the elements in the given set (1) x;x&lt;3 and x∈z

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: Let G=Sg. 14 xy= 0 for XiyE 4G, would if X=0 or y=o hoppen! 4 true, prove it l4 true, prove it;…

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Q: If E, and E2 are measurable then (E,UE,) is not measurable .

A:

Q: Suppose P(A)= 4, P(B)= .5, following: Find the P(ANB) a. b. P(A'nB) с. d. P(A'UB') P(BA)

A: Comments: As per our guidelines we are supposed to answer only first three subparts. Kindly repost…

Q: -dz < 2re?. z + 1 Jェ-1|=1

A:

Q: Let f(x.y) = In ( x2 + y ). If f,(2,a)=f,(- 1, 2), what is the value of a? O a. 6 O b.3 O. 7 O d. 8…

A:

Q: =gers and

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Q: a) Find the values of A and B if - {(x² + Ax + B)e*} = x²e* dx Hence, evaluate S, x²e*dx

A:

Q: 2.14 Use the identity EijmEkim = daðn – dad to show that a x (b x c) (a c)b- (a b)c. %3D

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: and xe"y %3D For ay

A: To find out partial derivatives.

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…

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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: Suppose A = (a, 0, 2) and B= (6, –2, b), for some a > 0 and b> 0. (a) If projĄB = 12 24 =,0,), find…

A: Suppose A=a, 0, 2 and B=6, -2, b, for some a&gt;0 and b&gt;0.If projAB=125, 0, 245, then to find the…

Q: Let U = x'e . Find dU .

A: The given function is: U=x2eyx Therefore: dU=∂U∂xdx+∂U∂ydy

Q: cha a_i, =aFor a in S, we denote its it h com ponent by ival ently, we have = (al; : : : ; an)…

A:

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

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Q: 8. Approximate 3.9996 using linearization.

A:

Q: Let X=(1,0, – 1,-V2)'. Then, ||X||2 = Select one: а. 3 O b. 4 C. 2 O d. 1

A: