Problem Set 12s

# 0 41 4 sin 4 x 4 cos 4 x lim lim 2 2 x 0 tan 5 x x

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x # & x sin x = − lim % ( x→0 \$ x cos x + sin x ' 0 again this is of type , apply L'Hospital's Rule again. 0 f. x2 +1− 6 =5 x →2 x−2 lim ln x sin πx Solution: ln x H 1/ x 1 1 lim = lim = = − x →1 sin πx x →1 π cos (πx ) π (− 1) π ln x 1 lim = − x →1 sin πx π sin 4 x c. lim x → 0 tan 5 x Solution: 0 This limit has the form . 0 4(1) 4 sin 4 x 4 cos 4 x lim = lim = 2 = 2 x →0 tan 5 x x → 0 5 sec (5 x ) 5 51 sin 4 x 4 lim = x →0 tan 5 x 5 1 ex −1− x − x2 2 d. lim 3 x →0 x Solution: 0 This limit has the form . 0 12 ex −1− x − x x x Hx H 2 = e − 1 − x = e − x = lim e lim x →0 x→0 6 x3 3x 2 6x 1 = 6 1 ex −1− x − x2 1 2 lim = 3 x →0 6 x lim x →1 # & # & x sin x x cos x + sin x − lim % m ( = − lxi→0 % ( x→0 \$ x cos x + sin x ' \$ − x sin x + cos x + cos x ' 0+0 =− =0 0 +1+1 1 ⎞ྏ ⎛ྎ lim ⎜ྎ cot x − ⎟ྏ = 0 x → 0⎝ྎ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online