m2 2. Prove that lim -+0n3 + 1 -=0. 3 5 100 3n2 + 2n - 1 3. Prove that lim = 5n2 +8 cos(n) 4. Prove that lim = 0. n-700 m2 + 17 5. Prove that lim (Vn+1 - Vn) = 0 Hint: Multiply Vn+1-vñ by 1 in a useful way. In particular, multiply Vn+1-17 by Vn+1+vn
1. Find 7(5") 3" 5n+12n+1 sin(n!) lim (a) im (b) n 2018 пH0 п2 n oo _ Зп? + п + 4(3") nt T lim sin (d) (с) lim 1 - 2n 3п — 2п n oo n oo 2. Let (an), be a sequence such that lim an n oo L. = 1 (a) What is lm an+1? пH00
40 Show the following results. 1-e2 (e) lim(2+3-12)tan(/4) (24.3)-4/ 2 (a) lim -+0 isin(3r) エ→2 3 (f) lim(cos x)In | = 1 エ→0 1+ tanz1/sin z 1+ tanh r (b) lim = 1 -+0 nT nT (g) lim cos no0 +sin 6n+1 (c) lim (sin r)1/(2r-) - 1 エ→/2 = e 3n+1 2 + sin r 1 (h) lim 0. (d) lim エー→0 1 In (1 - V-1) - . 2 In(cos x) r+1+ 40 Show the following results. 1-e2...
2. Prove that lim (-1)"+1 0. 72-00 n 2n 3. Prove that lim noon + 1 2. 80 4. Prove that lim n-+v5n 0. -7 9 - in 5. Prove that lim n0 8 + 13n 13
100 1. (a) (3 pt) Find the value of A such that lim (Vn? + (24 – 1)n +1 – Vn? +2n) = 0. (b) (3 pt) Find the value of B such that lim (Vn* – 5Bn2 +1 – Vnd – (B+ 2)/2) = 1200
2n2-31+1 b. lim cos 1. Find the following limits: a. lim 1 00 --- 3n2+4 n-00
PLEASE SHOW WORK!!!!!! 9) Find the value of the expression. a. cos arctan -- b. tan(arcsin(x)) = 10) From a point on a cliff 85 feet above water level an observer can see a ship. The angle of depression to the ship is 40. How far is the ship from the base of the cliff? sec? x 11) Verify the identity: -tan’x = tan x cotx 12) Find all solutions algebraically in the interval [0, 2T): sec? - 3 tan...
(B)(C)(D)(E)(G)(I)(J) 39 Write the Taylor expansion of function f order n at to given below. 1 (a) (g)2+v1+ I, n 2,ro - 0 n = 7, xo = 0 1 -2-3 (b) sin z cos(2x), (c) z In(2+3z), VI+I n= 3, To = 0 1 +e-1/ (h) 2+x n =5,xo= +o0 n= 3, ro = 1 T (i) cos (2r), n 4, xo= 6 (d) n = 7,xo = 0 COSI i) V+-VI3-, n 4, 1o =+00 (e) In(1+ arcsin(2r)),...
1. Given A = arcsin and cos B= 1 31 3' 2 <B<21 Find the exact value of sin(A+B).
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...