Show that if (Sn.tn) converges to (s,t) in R² with the do ("max") metric, then the sequence converges to the same limit in the usual d₂ metric.

Q: Verify that the following polfs have the indicated hazard function h+(+) = lim Pl=&T +) бэо 8 hy (t)…

A: Hazard function

Q: Suppose H(t) = t3 + t2 + 8t + 1. Find the limit lim t→1 H(t) The value of the limit is?

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Q: Let X = C[0, 1] be a metric space with metric d(f,g) max {f(x) = g(x)}. x[0,1] Prove that the…

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Q: By computing the limit of right-endpoint approximations, prove that b4 x' dx 4 if b > 0, then

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 2. Prove mx+b=mc+b   using the definition of a limit of a function where fx=mx+b is a function where…

A: Definition of limit: Let be a function. If for every there exists such that and we can write it…

Q: Compute lim n · (Vỹ – 1). | n→∞

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Q: Find the limit, if it exists, or type 'DNE' if it does not exist. lim ev22214y? (1,1)>(4,0)

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Q: Show that if (sn,tn) converges to (s,t) in ℝ2 with the d0 ("max") metric, then the sequence…

A: Metric on R2:d0((x,y),(a,b))=max{|x−a| , |y−b|}d2((x,y),(a,b))=(x−a)2+(y−b)2A sequence {xn} in a…

Q: What is the limit of f (x) = 1 as x → π?

A: The value of this function is equal to 1 regardless of value of x as we can see below in graph.  So…

Q: 6) a) show that Sx dx is divergent b) Show that Lim = 0. This shows we canuat xdx -- define = im…

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Q: Let X = R' and d be the metric on Rº given by d(x,y) = E., \x - y,| where x = (x, X2, Xa) and y =…

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Q: V5+s-V5 lim s→0 S

A: lims→ 05+s-5s=lims→ 01s+5+5Plug in the value s=0=10+5+5=125

Q: * 15sin(t*)dt Evaluate the limit lim

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Q: In R² with the standard topology, describe the limit points and closure of the set S = {(x, sin(-))…

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Q: (0, 1) = U(4 ",1– 4 ") n=D1 (Hint: taking limit is not acceptable)

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Q: 13. 0.) Compute limit fix, if it exists, for the following f: IR→IR ₁ × → 1×1₁ X ₁ = 1 x cases!

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Q: 4) State the limit definition of the derivahve. f'(x) =

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Q: Find the limit analytically

A: Given, limit function is

Q: 9. For each n E IN, let Xn be the set of polynomials of degree equal to n, and let Pn = U_0 Xk. True…

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Q: Evaluate the following limit. 9t lim 2e i tk t oo t+4J+ tan

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Q: Use the definition of a convergent sequence to show {7-4/n} n=1 to infinity, converges to 7 where…

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Q: 1. A company that manufactures computers has established that, on average, a new employee can 50t…

A: given N(t) = 50tt + 4where N(t) = assemble components per day after t days

Q: For i = 1, 2, ..., let X; ~ U (0, 4), and Y; ~ N (2, 4), independently. Find, E (X;) E (Y;) the…

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Q: Find the limits in Exercis

A: To find the limit of limθ→01-cos θsin 2θ, substitute θ with 0 and the indeterminate form of limits,…

Q: A material transmutes 50% of its mass to another element every 10 years due to radioactive decay.…

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Q: Our aim is to show that lim cos i does not exist. To do so, we will use the Divergence criteria.…

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Q: VI+2x — V1 — 4х 25. lim e* — 1 — х 27. lim .2

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Q: Let YN == √N+1' - N' for NEn. Show that Find the limit. (UNY) Converges.

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