2. in the following, sequences (an) are given. determine whether or not the sequences converge, and if so, determine limn? ooan with proof. reviewing practices 3.23, 3.25, and 3.30 may be . as . printing is for personal, private use only. no part of this book may be reproduced or transmitted ill be prosecuted. sequences and their limits 121 3 1 for odd n, 0 for even n. (a) an= b) an c) aln (d) an (hint: see 2 2n+1 1 for even n. 2n-1 n2 for odd n, exercise 11. n for even n. n. hnt rationalize.

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

96 39 cause 135 -96=39 im smart (i used a calculater)

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)