2.68 Suppose fn(x) = 1-". Decide whether or not f, converges uniformly on each interval, and prove your conclusion. a) (0, 1) c) [0, 6], where 0

Q: a, n = n 3n+1 3n-1 A) convergence C) test fails B) divergence O ооо

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Q: sin N 8) Show that converges/diverges.

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Q: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

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Q: Find P (-1.5 < or equal to Z < 0.2) where Z ~ N (0,1)

A: We will use Standard Normal table to find the required probability.

Q: 28. (Continuation of Exercise 27.) If E=1an converges, and if 1 > a, > 0 for all n, show that E=1 In…

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Q: a) Does f() -Σne" n=0 converge or diverge for r > 0? b) How do you know?

A: According to ratio test, if the limit L&lt;1, then the series converges and if L&gt;1, then the…

Q: 3. Define fn on (0, 1) by fn(x) = x". Show that fn converges to the constant function 0, but that…

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Q: 3 3) The Sequence of real function f(x) = x²+³ converges over a interval [1,1], dotally from th…

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Q: Find the interval of En=o 2"(z – 3)" O (3.5, 0) O (2.5, 0) O (2.5, 3.5) O (2, 3)

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Q: The seguence of function fn: x→x"+exp (x^) on [o,1] Then [0,1] we have: (fn) on ) neither conuerges…

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Q: Suppose that we observe that X1, X2, . . . , Xn  are iid∼ U(0, 1). Show that X(1) converges in…

A: A sequence of random variables Xn is said to converge in probability, denoted as Xn→pX, if…

Q: 7. has a fixed point. ) Prove that if f is a continuous function from [2, 5] to [2, 5], then f

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Q: -10 -9 -8-7 -6 -5 -4 8 -7 -6 -2 -1 5 4 3 2 1 -1 -3 & 1 2 3 4 5 Graph of f 67 8 9 10

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Q: 1) In order to use the integral test, we must verify that the sequence is decreasing (and positive…

A: We have to test series is convergent or divergent

Q: a)Find the average of the function f(x)= x² +1 on the interval [-1,2] Answer:

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Q: suppose that X~N (3, oʻ), AP (3<X<6) =0.4, then P(X20)= A.0.4 B.0.9 C.0.6 D.0.1

A: We have to find given probability.

Q: let f(x) = 2x²-36x² + 20. Find the intervals where f is increasing. a) (-3,0)√(3, ~) b) (-3,0)0(0,3)…

A: Let To find the intervals where  is increasing.

Q: CK Show whye* dx does or does not converge.

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Q: Q.2) Determine of each point convergens or diverges: (-1)"(3n)!/ /n! (n + 1)! (n+ 2)!

A: determine whether the series converges of diverges (i) ∑n=0∞-1n3n!n!n+1!n+2! we will use ratio test…

Q: 10. Consider a continuous function f with the properties that f is concave up on the interval [-1,3]…

A: Solution (10) :::    Given,  f is concave up on the interval [-1,3] and concave down on the interval…

Q: Let T: (X,d) (Y,d) be a continuous function for all n. If {T,} converges uniformly to T on X, then T…

A: Given Tn:X,d→Y,d^ is a continuous function for all n and Tn converges uniformly to T on X. We have…

Q: value of for which Are there cmy value f converges.

A: We know that a series is said to be convergent if the sequence of its partial sums converges. Using…

Q: I En=1 an converges then 2a, converges.

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Q: 6. Use the Mean Value Theorem to find all values of c in (6, 14) such that f(b)-f(a) f'(c) = for…

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Q: Use the {\bf Cayley Hamilton Theorem} to come up with an expression for A" in terms of n when 1 A =

A: As you have asked more than one question, we shall answer first Que only. For others kindly post…