Show epsilon arguments for any limit proofs: 1)Prove: If limf(x)x->a=L and c∈R, then limx->acf(x)=cL. 2) Prove:...

Show epsilon arguments for any limit proofs:

1)Prove: If limf(x)_x->a=L and c∈R, then lim_x->acf(x)=cL.
2) Prove: If lim f(x)_x->a = L and lim g(x)_x->a = M, then lim(f(x)+g(x))_x->a = L+M.

3) Find a counterexample to the converse of #2.

4) Prove: If lim f(x)_x->a = L and lim g(x)_x->a = M, then lim(f(x)g(x)) _x->a= LM.

5) Find a counterexample to the converse of #4.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

prove by epsilon-delta definition that f:R->R given by f(x)=x^3 is continuous at x=2

prove using limit lemma that n^2 > nlogn given some epsilon > 0

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this...

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this is indeed the correct limit. (b) Use an epsilon, N argument to show that {1/(n^(1/2))} converges to 0. (c) Let k be a positive integer. Use an epsilon, N argument to show that {a/(n^(1/k))} converges to 0. (d) Show that if {Xn} converges to x, then the sequence {Xn^3} converges to x^3. This has to be an epsilon, N argument [Hint: Use the difference...

Prove (a) that ψ ± = N (x ± iy)f(r) is an eigenfunction of L^2 and...

Prove (a) that ψ ± = N (x ± iy)f(r) is an eigenfunction of L^2 and Lz and set the eigenvalues corresponding. (b) Construct a wave function ψ_0(r) that is an eigenfunction of L^2 whose eigenvalue is the same as that of a), but whose eigenvalue Lz differs by a unit of the one found in a). (c) Find an eigenfunction of L^2 and Lx, analogous to those of parts a) and b), which have the same eigenvalue L^2 but...

Using the epsilon-delta definition prove Lim of x^2 =4 when x approaches 2

Let f(x) and g(x) be two generic functions. Assume limx→0(f(x)+2g(x))=2 & limx→0(f(x)−g(x))=8. Compute limx→1(f(lnx)/g(x2−x)). A. It...

Let f(x) and g(x) be two generic functions. Assume limx→0(f(x)+2g(x))=2 & limx→0(f(x)−g(x))=8. Compute limx→1(f(lnx)/g(x2−x)). A. It cannot be computed B. 2 C. 4 D. -3 E. -4

1)For the function f(x)=6x^2−2x, evaluate and simplify. f(x+h)−f(x)/h 2)Evaluate the limit: limx→−6 if x^2+5x−6/x+6 3)A bacteria...

1)For the function f(x)=6x^2−2x, evaluate and simplify. f(x+h)−f(x)/h 2)Evaluate the limit: limx→−6 if x^2+5x−6/x+6 3)A bacteria culture starts with 820820 bacteria and grows at a rate proportional to its size. After 22 hours there will be 16401640 bacteria. (a) Express the population PP after tt hours as a function of tt. Be sure to keep at least 4 significant figures on the growth rate. P(t)P(t)= (b) What will be the population after 8 hours? bacteria (c) How long will it...

prove the sufficiency, let L be any closed contour in region R occupied by field A,...

prove the sufficiency, let L be any closed contour in region R occupied by field A, suppose curl A=0 everywhere in R. then, since R is simply connected. L is the boundary of some surface S lying entirely in R. By Stoke's theorem, integral of A =0. prove that A is a potential field. ( potential and irrotational fields). please in details thx:)

Player 1 chooses T, M, or B. Player 2 chooses L, C, or R. L C...

Player 1 chooses T, M, or B. Player 2 chooses L, C, or R. L C R T 0, 1 -1, 1 1, 0 M 1, 3 0, 1 2, 2 B 0, 1 0, 1 3, 1 (a) Find all strictly dominated strategies for Player 1. You should state what strategy strictly dominates them. (b) Find all weakly dominated strategies for Player 2. You should state what strategy weakly dominates them. (c) Is there any weakly dominant strategy for player...

Let L = {x = a r b s c t | r + s =...

Let L = {x = a r b s c t | r + s = t, r, s, t ≥ 0}. Give the simplest proof you can that L is not regular using the pumping lemma.

Subjects