University:
Georgia Southern University
Course:
MATH 1441 | Calculus I
Academic year:

2024
Views:

322

Pages:

5
Author:

Jalen W.

"" it 2-1 °n2ñ -21T Chapter 2: Limit of a function: y=si¥ Limits of Trigonometric Functions, Limits involving 8=6 𝑠𝑖𝑛 𝜃 𝜃→0 = 1 (𝜃 in radians), 𝜃 𝜃→0 o → 0 𝜃 : £35,31T] [-1/2] ' . ; si = b) lim 1−𝑐𝑜𝑠 𝜃 𝜃→0 Ex. 5 / Page 87: Show that lim Ui 𝑠𝑖𝑛 𝜃 ← Theorem/ Page 68: a) lim = 𝑠𝑖𝑛 2𝜃 5𝜃 0+0 = 𝜃 = 0. 2 = . 5 bi . •→ hi . 3€ 2£ Y:-) -1 :-) 2-5 . hi siz÷ It , 20 =Y → 0 as • →o Find the limit: 𝑠𝑖𝑛 3𝑥 lim 1. ^ 4𝑥 𝑥→0 } } ) %÷ ¥:( . = ¥141 " -4¥ -5¥ . - %÷= :-& 𝑡𝑎𝑛 2𝑥 lim 2. - 4mi ✗→ ✗ , 𝑥 𝑥→0 = =p;] 0 Sind " " ce Ami suing . ✗→ co¥ . = 2X 0 Ami =) 2x→o =¥÷÷÷× = leni ✗→ = - of"¥ . . ¥ Uni ✗→ 0 1- = coax # =/ Therefore ÷§¥¥¥×→¥× ten him I = = (2) (1) ① ?⃝ " 3. = lim 𝑥 𝑐𝑠𝑐 2𝑥 𝑥→0 cos 5𝑥 ✗→ ÷÷ :÷:÷÷ 4mi Quotient Rule Uni hni 4. lim 𝑥+𝑥 cos 𝑥 𝑥→0 sin 𝑥 cos 𝑥 =¥¥% = 1¥11 ":÷] ¥ .EE?::---fY-.is:-xX:Io'+:# ( t ) ( 2) = = 12J nice cos 0=1 ) 5. lim tan 2𝑥 = 𝑥→0 tan 𝜋𝑥 s%¥× = • 2×4.18*1-1 "^ ÷;¥ 777 ¥ → . (2) I 4,1¥ . =Y 6. lim SX 8𝑥 ' ¥✗- ✗ 𝑥→0 3 sin 𝑥−𝑥 :-X :-X :¥ = = ÷¥- -7 ÷ 6in - I as , =D ✗ to 5m¥ ✗ → o = I #65/ Page 72: It can be shown that the double inequality is satisfied for all 𝑥 close to zero: 1 − 𝑥 sin 𝑥 Find lim 𝑥→0 2−2 cos 𝑥 𝑥2 6 ≤ 2−2 cos 𝑥 ✗ → 0 ( ✗ → therefore hi ✗→ 1- , by ¥) (1) Uni and ≤ 1. . Uni since 𝑥 sin 𝑥 = I = 1 , 0 the sandwich = 0 I theorem ,

Chapter 2: Limit of a Function

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