Why is it false that
source: "Introduction to Analysis" by Arthur Mattuck p.158, question 11.2.3
Why is it false that source: "Introduction to Analysis" by Arthur Mattuck p.158, question 11.2.3 limf(x)-0 → li...
Real analysis
10 11 12 13 please
(r 2 4.1 Limit of Function 129 se f: E → R, p is a limit point of E, and limf(x)-L. Prove that lim)ILI. h If, in addition, )o for all x E E, prove that lim b. Prove that lim (f(x))"-L" for each n E N. ethe limit theorems, examples, and previous exercises to find each of the following limits. State which theo- rems, examples, or exercises are used in each case....
3. Suppose f : [0,) + R is a continuous function and that L limf(x) exists is a real number). Prove that f is uniformly continuous on (0,.). Suggestion: Let e > 0. Write out what the condition L = lim,+ f(t) means for this e: there erists M > 0 such that... Also write out what you are trying to prove about this e in this problem. Note that f is uniformly continuous on (0.M +1] because this is...
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
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6) The following statement is false: If so f(x)dx 2 0, then f(x) 2 0 for all x in [a, bl. Give an example that shows why this statement is false
6) The following statement is false: If so f(x)dx 2 0, then f(x) 2 0 for all x in [a, bl. Give an example that shows why this statement is false
Given that lim F(x) = 0 lim g(x) = 0 lim h(x) = 1 Jim P(x) = lim (x) = .. evaluate the limits below where possible. (If a limit is indeterminate, enter INDETERMINATE.) (a) lim [fix)] lim [F(x)] X (c) lim [h(x)]04) 8 [(x)] X lim P(x)] 20 X (1) lim "P(x) X Enhanced Feedback Please try again, keeping in mind that the indeterminate cases are 0.9, 03.00,60,1", and " - .. Need Help? Read It Talk tea Tutor...
6. Justify briefly (max two lines) if the following statements are true or false. Answers with just Tor F won't receive any points. (a) (1 point) The curve with vector (Cartesian) equation r(t) = (t cost, tsint, t) lies on the surface with cylindrical equation 2 = 72 (b) (1 point) If ñ x p=0 then ñ = 0 or p=0. (c) (1 point) 24 – 4y2 lim (x,y)+(0,0) 22 + 2y2 = 0 (d) (1 point) If f(x, y)...
(d) The function f(x)1 is locally integrable on (0, oo). To see whether converges, we consider the improper integrals separately. (The choice of π above is arbitrary.) By considering f (x) lim an show that 11 converges iff p< 1. Next, by considering lim J(z) an -p- dx show that /2 converges iff p +q>1. Finally, combine these results to show that I converges iff p < 1 and p+q1.
(d) The function f(x)1 is locally integrable on (0, oo)....
real analysis
1,3,8,11,12 please
4.4.3
4.4.11a
Limits and Continuity 4 Chapter Remark: In the statement of Theorem 4.4.12 we assumed that f was tone and continuous on the interval I. The fact that f is either stric tric. strictly decreasing on / implies that f is one-to-one on t one-to-one and continuous on an interval 1, then as a consequence of the value theorem the function f is strictly monotone on I (Exercise 15). This false if either f is...
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...
(8). The one dimensional neutron diffusion equation with a (plane) source at x-0 is d'f(x) n (2) +002 f (x)-00(x) dx where f(x) is the flux of neutrons (f(x)→0 as x→±o), Q δ (x) is the (plane) source at x-0 (5(x) is the Dirac delta function), and o is a constant. This problem involves finding the solution to this equation using Fourier Transforms. You may use the formulas derived in class for the Fourier Transform of derivatives, but otherwise compute...