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Q: show that }I f,lm) Ck-m) 2.

A: For, ∑m=0kf1mf2k-m, substitute k-m=n or m=k-n: ∑m=0kf1mf2k-m=∑k-n=0kf1k-nf2k-k-n…

Q: +5v

A:

Q: C. Show that both R and R² may be covered by countably many open balls.

A: Firstly we have shown that R may be covered by countably many open balls. Let us  consider the set…

Q: S 289 xe

A:

Q: sst. Let f(x, y, z) = x³ yª + zª and x = s5, y = st³, and z = s

A:

Q: Let r ERQ. Prove that for all a, b, c EQ, =cr iff a = 0 and b = c. a + br

A: Given that r∈RQ Let a,b,c∈Qa+br=cr iff a=0 and b=c

Q: Let A,BE Mmna Shaw that vTAw= V' Bw for all VER™ end WEIR" if and only if LA=B. %3D

A:

Q: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: When is S \ T = T \ S for sets S, T? Give an example

A:

Q: t3 dt 6) f Vt2 + a?

A: Given Data The integral is     Let,

Q: End the cquation ot the perpeadicular to tie line KEy=4tat goes thousn the point (0,2).

A: topic - equation of perpendicular line

Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

A:

Q: What are the consequences of the violation of the OLS assumption cov(x;, e;) = 0?

A: A linear Regression  model consist of one dependent and one independent  variable.

Q: Ex:Let (Q,0)be a slouP. A nodremp ty set HS Q - is a Sab sYou? of G if and on ly if ab" E He fer anS…

A:

Q: Let z = 6ex²y³. Then: дz дх дz ду

A: We can solve this as follows:

Q: Is 1z = 1 for all z ∈ C?

A:

Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

A:

Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.

A:

Q: WORX Gavlen flw)=x-d g6)= V-(x-6)" WOP Mekong Delta Find the derivatve Nlx) guven

A: Given:- f(x)=x-2 g(x)=4-(x-6)2+2 h(x)=x-6 We have to find the λ'(x)=? Given that,…

Q: 15) Find u x v for u = and v = .

A: Given vectors are, u = -7, 1, 12 = -7 i^ + j^ + 12 k^v = 2, 2, 3 = 2 i^ + 2 j^ + 2 k^

Q: If z, w E C, prove that z+w=z+w.

A: This follows from simple substitution. The detailed solution is presented in step 2. As requested i…

Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

Q: Prove that dv du 2 – u? + v² 18

A: