Suppose that the functions and g, with L and La at r a as shown below. approximations Then lim a9(x A) C) 2. D) 3. E) There is not enough information to conclude any of the above.

Q: Compute the following limits if they exist. sec r – 1 (a) lim z-40- 23 I – sin r (b) lim 1+0 x - tan…

A: L. Hospital RuleIf limx→a f(x)g(x) = 00 or v6c6 formThen differentiate f(x) & g(x) and take…

Q: Show that (2o + h)" – 2ö = nz- | n-1 lim h→0 h for any zo E C.

A: To show: limh→0z0+hn-z0nh=nz0n-1for any z0∈ℂ

Q: Find the limit (if it exists).

A: If the vector valued function is of the formr(t) = f(t)i + g(t)j + h(t)kThen its limit is given…

Q: Compute the following limit: 1-cos 2z 1. lim I→0 z sin 2x· Hint: 1 – cost = 2 sin? t.

A:

Q: Which of the following is equal to the limit limx→0 sin^2 2x/xtanx A.  0  B.  4  C.  2  D.  8

A: We have to find the limit Use l'hopitals rule to obtain the limit. Keep on differentiating the…

Q: evaluate using Theorem 2 as necessary.

A:

Q: 5. If b > 0, prove that lim = 0. %3D 1+nb

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: What is lim m→0 sin(m) m ?

A:

Q: Use l'Hôpital's rule to find the limits 20 - T 30 + T 17. lim /2 cos (2T - 8) 18. lim 0--1/3 sin (0…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 7 sin(T2) In (zº) q(z) = %3D What is lim q(x)? ncwor bolow:

A:

Q: Find the limit. lim e 3t i е j + Sin2 tan(5t) k) t 0

A: The given expression is,

Q: Compute the indicated limits. 2x + 5 lim cos 3x? + 2x – 5

A:

Q: Evaluate the limits: lim (cosx)cor*x 13. Ans: e12

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 7. lim x* sin 4 x>0

A:

Q: 7 Find lim cos - Enter I for o, -I for –∞, and DNE if the limit does not exist. Answer:

A: Given query is to find the limit of the expression.

Q: Show that the following: If r > 1, then lim Vr – 1 = 0.

A:

Q: In R² with the standard topology, describe the limit points and closure of the set S = {(x, sin(-))…

A:

Q: Calculate the following limits, if they exist. lim (7,y)→(0,0) 1 – cos(x² + y²) 1² + y²

A: Use the polar coordinate substitution

Q: Find the value of the following limits: 5y 1-limy→0 tan 10y

A:

Q: Use L'Hôpital's Rule to calculate the following limits. sin r + tanr 1² – 1 te (a) lim (b) lim Inr…

A: "Since you have asked multiple questions, we will solve the first question for you.  If you want…

Q: Find the limits in Exercis

A: Given: L=limx→0x-xcosxsin23x

Q: Question 2 5x limr→-0 g² + 10x – 1 c→-∞

A:

Q: I/ find the limit of the following: 1- limx cos 2- lim V +x sin

A:

Q: Use the Squeeze Theorem to show that lim a sin (1/r) = 0. Show all %3D work. 2.

A:

Q: lim; 0 (, cos t, In t). t+1

A: limt→01t+1, cost, lnt

Q: 27. a. Show that the area A, of an n-sided regular polygon in of radius r is a circle sin nr2 2т A,…

A:

Q: Find the limits in Exercises

A: Given: limx→∞x57+x-3x57+cos x   ……1

Q: 2 Show that the following limit does not exist. lim Ty Cos y (r.9)-(0.0) 3r+ y²

A:

Q: Find the limit of the following. V3 sin 0 lim 0→t/3 3

A:

Q: 1. Prove that lim vx sin O using the Squeeze Theorem.

A: Using squeeze theorem,

Q: Show that when T(z) = az+b cz+d where (ad - bc ‡ 0), find lim T(z) = ∞ if c = 0. 7-3

A:

Q: [4] (a) Show that lim (xa)-(0,0) 2x+y? y-mx, or along any parabola y= exists and it's approaches to…

A:

Q: Evaluate the following limits. sin- (e") 1. lim 2 V1- e20 1 1 x + sin 2. lim

A: On solving this we will get

Q: Find the limits

A: Limit: limθ→∞cos θ-1θ

Q: Let f(2) = C, be the upper half eircle J2| = R in the counterclockwise direction with R>1, and /= ,…

A:

Q: Show that the limit does not exist. xy? - 1 lim (Ky)→(1,1) y-1

A:

Q: Evaluate the limit. lim (sin(4t)i + cos(5t)j + tan(2t)k)

A:

Q: d cos x = – sin x - dx

A:

Q: The result of the following sin 1² t limit is lim 1-0

A:

Q: Evaluate the following limits by constructing their respective table of values. 1- cos(3t) 4. lim 3t…

A: note: as per our company guidelines, we are supposed to answer 3 sub parts of a given question.…

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

A: Given, limx→01x sinx-1x2

Q: ind the following limit. x2 + 1 lim (x, y) - (0, 15) arctan + (y – 15)2,

A:

Q: Evaluate the following limits by constructing the table of values. 1. lim -cos(3t) 3t t--0 f(t).…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: To apply the divergence test for Σ „5/4n² n=1 we need to evaluate lim eS/4n?. n→∞ What is the value…

A: Here we have to find the value of the limit.

Q: Find the limit 1- sin z In (100r² + e*) (a) lim (b) lim 1+ cos 2r 100z

A:

Q: 1 – cos(x² + y?) x2 + y? - lim (x,y)→(0,0)

A: Given lim(x,y)->(0,0)1-cosx2+y2x2+y2 find out the limit if it exists

Q: cos t – cos² t Evaluate lim t→0 t

A: →When limit is of the form 00 or ∞∞, then L'Hospital rule is used.      In this rule take the…

Q: Prove the following result: lim csc 0 – cot 0 = 0 0→0

A:

Q: 1. Consider {a} where a, = tanh(Vn). Use our rigorous definition of the limit to prove that lim…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…