SEATWORK: Evaluate the following limits 1. lim (sinx)/(cos x - 3) 6. lim (sin 3x +2)/(cos x) x>TT/6 2. lim COs 5x 7. lim (sin 5x)/(5x) x>T/5 3. lim sec 2x 8. lim (sin 4x)/(x) 4. lim cot (x/2) 9. lim (1 -cos8x)/4x X

Q: Figure out the following limits. (No L'Hopital Rule) 2x sin x-a b. lim a. lim 1-0 sinr - tan a -a…

A: Given

Q: Find the limits. Are the functions continuous at thepoint being approached? lim x →1 cos-1 (ln √x)

A: We find the limit by substitution

Q: If f(x+y)=f(x)+f(y) for all x , y e R and E(tanx) _ 2f (sinx) f (1) =1,then evaluate lim x’f(sinx)…

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 4. Lim Arctanx, x-0\x

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Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x 4 A) 을 B) 0 530 C) D) Does not exist

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Q: Q1) Find the followings limits;: (Answer 4 Only) 1. lim 2.lim 25x (cotx)(cse5x) 3x 5-lim tanx-sinx…

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Q: 2) Show that sinax _a lim x-0 tanbx b %3D

A: Show that  limx→0sinaxtanbx

Q: sin(In r) 5. Use the Squeeze Theorem to evaluate lim 1-40+ In (sin z)*

A: Solution is given below:

Q: Find the limit of the trigonometric function.

A: Given: limx→π2sin x To Find: The limit of the given trigonometric function

Q: Evaluate the following limits. 2x sin- x 1. lim х-0 еx — х — 1 2. lim (sec x)cot × X-

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Q: sin xy lim 0.

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Q: True or false: lim(sin) as x goes to infinity exists.

A: Given, limx→∞sinx Find in the following that this limit is exist or not.

Q: Find the value of each limit: 1- cos x а. lim x→0 x+x b. lim sin(x+ h) – sin(x) h h→0

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Q: Use the Squeeze Theorem to evaluate lim sin(ln x) csch(cot x). x→0+

A: Given:                                                                fx:=sinlnxcschcotx. To do:…

Q: Compute the following limits if they exist. sec x – 1 (a) lim I0- x – sin a (b) lim I40 x – tan x 2…

A: "Since you have posted a question with multiple sub- parts, we will solve first three sub -parts…

Q: Find the limits. Are the functions continuous at the point being approached?

A: Given function is  Since, the function f(t) exists finitely at t=0, so we will evaluate the limit…

Q: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: Find the limits

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Q: Q3. Compute the following limits if they exist. sec a - 1 (a) lim x – sin r (b) lim 20 x - tan r 2 –…

A: Q.3 part a) Substituting the limit in function, This is indeterminate form 0/0,

Q: II. Evaluate the limits. tan 0 2. lim 0 -0 sin 20 (y-#)* 2. 4. lim t 1-sin y y - 2 2.

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Q: 02.) Find the limit lim X+x cos X sin x cos x 1- X→0 lim sin 5x SIn 4x 3-

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Q: Q2.) Find the limit lim X+x cos x 1. X→ 0 sin x cos x

A: We find limit x+ x cos x lim X → 0 Sn x cos x

Q: x 2 sinx Q1//A- f(x) = x <= COSX Required: lim f(x) 4

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Q: cos x D. Explain why we cannot apply L'Hôspital's rule to evaluate lim x-0

A: Given query is to find why L'hospital can not be used.

Q: Evaluate the limits sin3h-2h 4) lim sin?x 5) lim x 0 1-cos x

A: (4) limh→0sin3h-2hh=sin3(0)-2(0)0=00=indeterminate form Apply L'Hospital rule,…

Q: Q3. Compute the following limits if they exist. SEC x – 1 (а) lim x→0- sin x (b) lim x→0 x tan x 2 -…

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Q: Use l’Hôpital’s Rule to find the limits

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Q: Find the two limits: sin 2x lim r-T/2 COS x

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Q: C)Use LHospital's rule to evaluate only two of the following limits (if exist): 5⁰-6 lim (ii) lim…

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Q: Use l’Hôpital’s rule to find the limits

A: It is given that,limθ→0θ-sinθcosθtanθ-θ We have to find the limits using L'Hopital rule.…

Q: Compute the following limits if they exist. sec x – 1 (a) lim x – sin x (b) lim x→0 x – tan x 2 - VI…

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Q: Find the limits in Exercises 25–30. sin (1 – cos x) х sin x 25. lim x→0 26. lim x-0" sinVx sin (x² +…

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Q: IV. Do as indicated. Use Squeeze Theorem to evaluate lim sin(sinh x) csch z.

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Q: Evaluate cot x – cos x lim z¬7/2 (T – 2æ)°

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Q: Evaluate the following limits. 2 sin 5x a. lim x→0 3x b. lim sin 5x cot 3x x→0 d. lim (sec x – tan…

A: Hey, since there are multiple questions posted, we will answer first three question. If you want any…

Q: f(x) Consider the function: 9 sec z 18--7 tan x 9(x) What is lim f(x). I 9(x) -? Note: For limits at…

A: I have given this answer in step-2.

Q: Evaluate the following limits: x + sinx lim х-оо 2х + 5 lim - х-0 tan3x 1- Vx lim x-1 1 - xX x. Sinx…

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Q: Use l'Hopital's rule to evaluate the following limits 1+cos(re *) (a) lim, »0 sin(x) In(x-1) (b)…

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Q: I. Evaluate the following limits: sinh(x2−x2) 1. lim x→0 sinh(x−x) 2. lim (x - ln x)* x+0+

A: The given problem is to evaluate the given limits of the given functions by checking the left hand…

Q: You may assume that the sine and cosine functions are continuous and may freely use techniques from…

A: (a).   We have to find the limit of:   limx→0 sin(2x)-2xx3

Q: 1. Find the following limits proving whether they exist or do not exist y² sin x X E) F) lim (x, y)…

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Q: 3. Compute the following limits. Justify your steps. 2t sin(x – 1) (а) lim t→0 tant (b) lim I→1 x2 –…

A: Answer of (a). 2 (b). 1/2

Q: (a) lim θ→0 θ tan(θ) (b) limx→π sin(x) x − π (c) lim t→0 sin2 (5t) t 2

A: Given that : a) limθ→0 θ tan (θ) b) limx→π sin (x ) . ( x - π) c ) limt→0 sin2 (5t) . t2

Q: Evaluate the limit. sin(x + h) – sin x lim

A: Applying the limit: Since the limit is in 0/0 form, L'Hospital rule can be applied.

Q: 1 lim x→0 x sin x x2 О 14 O 1/7 О 16 O 1/5

A: To find limx → 0 1x sin x - 1x2

Q: Evaluate the following limits if they exist. 1 — х — е" a) lim 2(1 — е") b) lim (1 + sin x)'/= sec x…

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Q: Find the limit. 2. (2 sin x+2 cos´y+4 sec lim P→(2,2,0)

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Q: Find the limits limx→0+sin x . ln x

A: The given limit is: limx→0+sinx·lnx  Consider "h" is a too small positive real number,  Then,…

Q: Compute the following limits if they exist. sec r - 1 (a) lim I0- r3 x – sin x (b) lim I0 x - tanr 2…

A: We are entitled to solve 3 subparts of first question so, I am providing you the solution of the…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.