8. Compute the limit arctan 2x lim +- X (a) 0 (b) 7/2 (c) –7/2 (d) e (e) 1
2.13.2 Compute lim sups and lim infs for the following sequences (a) {(-1)"n} (b) {sin (nT/8)} (c) {nsin (nt/8)} (d) {[(n + 1) sin (n7/8)]/n} (e) {1+(-1)"} (f) {rn} consists of all rational numbers in the interval (0,1) arranged in some order.
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
Use Taylor polynomials to evaluate the limit. e-3x – 1 7) lim X0 х sin 2x - sin 4x 8) lim x>0 х
- 3e - sin(-5x) Find lim - 2x (x,y)+(0,0) -3e - sin(-5x) lim - 2x (x,y)-(0,0) (Type an integer or a simplified fraction.)
Unit D: Applications of the Derivati 8. lim (cos(x))1/0 3 +0+ then det 9. lim (x + 5)3/22 xoo om Hits Ropa the NOTTE
Evaluate the following limits: x2 +7x - 14 a) lim 2x-5 b) lim tan(3x) - X = c) lim X+0 4x2-3r d) lim a "270 3x - 3xcos(2x) 2x2 sin(3x)
W60. Compute (sin x + cos x)(4 – 2 sin 2x – sin? 2x)e" dx sin 2x where = 6 (0,7) Mihály Be Pirkulyiev Rovsen W38. Let (an)n be a sequence, given by the recurrence: man+1 + (m - 2) an an-1 = 0 where me R is a parameter and the first two terms of (an), are fixed known real numbers. Find me R, so that lim an = 0 n-00 Tad
Problem 5: (15 points) (a) Find the limit sin(2x)-2c lim ェ→0 (b)Find the limit lim (sin1/x-/2) ι π /2
Problem 5: (15 points) (a) Find the limit sin(2x)-2c lim ェ→0 (b)Find the limit lim (sin1/x-/2) ι π /2
(18. a) Evaluate lim e sin (b) Evaluate lim x sin x 0 x (c) Illustrate parts (a) and (b) by graphing y = x sin(1/x).