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- 1- let f(x)= |x^2-4|/(x+2). Determine the limit lim_{x->-2} f(x), if it exist. 2- determine the limit lim_{h->0}[(x+h)2-x^2]/h by treating x as a constant. 3- dtermine the lim_{x->0} cos(2x)/x 4-determine the limit_{x->0} sin(2x^2)/xtan(4x)4. Find the limit, if it exists, or show that the limit does not exist: lim(x,y)→(1,−1) 3^−xy cos(x + y)How do I prove that the limit does not exist as (x,y)->(0,0) and x cannot equal 0. For (x^2 +4y^2) / x^2.
- Determine value for c so that lim f(x) x--> 3 exists f(x)= 1/3x+c For x<3 -x+8 For x>3Find an example of a function f : [−1,1] → R such that for A := [0,1], the restrictionf |A(x) → 0 as x → 0, but the limit of f(x) as x → 0 does not exist. Show whyDiscuss the continuity of the function and evaluate the limit of f (x, y) (if it exists) as (x, y) (0, 0).
- FInd A and B such that g(x) has limits at x= -1 and x=3Consider the function g(x) = cos(1/x). We will investigate the limit behavior at x = 0. c) If n is an arbitrary positive integer, find points x1 and x2 (int terms of n) in the interval(-1/n, 1/n( such that g(x2) = 1 and g(x2) = -1. d) Explain (in a brief paragraph) why (c) implies that g does not have a limit at x = 0. e) Where is g continuous? Justify your answer. You may use facts from the textbook in Section 2.2 - 2.5.evauluate the limit lim x→0 (sin2 (3x))/ x2
- TRUE or FALSE. If f is undefined at x = c, then the limit of f (x) as x approaches c does not exist.3. Let {gn} be a sequence of integrable functions such that gn →g a.e. with g integrable. Show that lim f [gn – g| = 0 if and only if lim f \gn| = S \g].Prove that a function f is continuous at a limit point p iff the limit as x goes to p is f(p).