Problem 2 1. Let fn(ar) n As the metric take p(x, y) = |x - y. Does lim, fn(x) exist for all E R? If it exists, is the convergence uniform. Justify 2. Consider fn(x) = x2m, x E [0, 1]. Is it true that lim (lim fn(= lim( lim fn(x)) noo x-1 Justify.
2. Solve for u(x,t) using Laplace transform (13.5.5) a(x,0) /ar f(x). =
2. Solve for u(x,t) using Laplace transform (13.5.5) a(x,0) /ar f(x). =
a Using f2) = e T42/22-1, show that noo cos CTTx/2) doc --T -00 JC2 | abc = -1 Ob Shad that to ex ebx (se - [cot (92) - Cat (67)] Hat eak Use a FR, TI) I-ex as rectangular conform with vernces at C-R,O) RO) and R, IT) with a Seme Carcle indentation at the origin.
(b) I G)(u) and G'(1) = 2+e Ft2): 3gcx1+1α)-x'(x) faf(x) , compute G(1) and G'(1). g(5a)' 2x for 37 Problem 2 For each function below, find the smallest integer n for which f)0 and find fin-(x) or explain why this is not possible. notation: The factorial function is n!n (n -1).(n-2)3.2.1 example: If (x)2+z2-1, then n 5 andf)24.3-2.1 2(41). (a) (x)95 16z +23. (b) f(x) sin(3z). Problem 3 3 is shown to The graph of the tilted ellipse z2 -...
Xy3 Question 2: a) Evaluate Tim (x,y) = (0,0) 3x2 + y4
PROVE: USING THE PRECISE DEFINITION OF LIMIT Tim ( 2-8x) = 14 *+- 3 2 show all work, other than using precise definition of limit, won't be accepted.
Graph the function fix) 2- for x 2 1 - 3x, for x 2 OA OB Ос. OD Click to select your answer 30 004
3x Find the limit: Tim In(x) x → 1 (X-1
(c) Let f :la,b- R be an integrable function. Prove that lim . (Your argument should include why faf makes sense for a < x < b.)
(c) Let f :la,b- R be an integrable function. Prove that lim . (Your argument should include why faf makes sense for a