Since this expression holds for all e, we must have fESSr. 25. Since fn

Q: b For any be R, use definition to prove that lim-=0. n

A:

Q: Let a,=l.cayider the sequeue fany generated It anti= an (a) Shaw that Lim an= Ø ,where Ø= !t v5 x…

A:

Q: X + 6х — 16 29. lim х—2 х2 — Зх + 2

A:

Q: Evaluate the given

A: We will use the below rule, So,

Q: Q);- Compute the following dimit if exist. they (i). limit 8+iZ3 Zai z²+4 (1). limit Rez 240

A:

Q: Evaluate limn→∞ n arctan 금.

A: Please see the explanation below

Q: 2f"(2-3h)-25"(z4 34) If G(z) lim, s0 and f(z) = Then G'(1) = %3D Select one: O -6 O -72 O 2 O -2 O…

A:

Q: 4. Let f RR and let cЄ R. Show that limf(x) = L if and only if lim f(x + c) = L. x-e x-0 PLEAEhelp…

A: The objective of this question is to prove that the limit of a function f(x) as x approaches a…

Q: Suppose the inequality (2² - 4x + 3) ≤ f(x) ≤ cos (#) Find lim fx if it exists. 3 x-2 OA) -1 OB) O…

A: We use sandwich theorem to find limit

Q: * 15sin(t*)dt Evaluate the limit lim

A:

Q: Show that if xn ≤ yn ≤ zn for all n ∈ N, and if lim xn = lim zn = l, then lim yn = l as well.

A: Given xn≤yn≤zn And also given lim xn=lim zn=l

Q: 2. Assume that lim så and lim të exist, and tn ≥ sn for all n. Prove that limtë ≥ lim sɲ. (hint:…

A: Given that exist and for all n.The objective is to prove that .

Q: Evaluate the following limit tan(3r³+3y³) lim (a)-(0,0) 62³ +6y³ O O O O O 1|2 2 0 + 32²-3y The…

A: In this question we will approach origin  from both axis and then check the value of limit. If value…

Q: My Probiems a. lim ee 00

A: we get infinity

Q: sec x lim sec(3x) X- 2 5х lim In(2+e*) х>о

A: Given:        limx→π2-secxsec3x we know that secx=1cosx         =limx→π2-cos3xcosx

Q: Compute the following limits if they exist ৪+ i2 Lim 2→-2i Lim Re 2

A:

Q: if (7- 2w) < f (w) < (7 – w²), for – 1<w < 1. Find lim f (w). w-0 2 O 7 O 4 O does not exist O O…

A:

Q: 7. Show that lim x³ = c³ for any c E R. X-C

A: To prove:- for any

Q: Suppose that E is an extension of F of prime degree. Show that, forevery a in E, F(a) = F or F(a) =…

A: Let E be an extension of F of degree p (prime) =&gt; [E : F] = p Here we will use tower property to…

Q: Evaluate: lim 1+ O 1 a 00 none of the choices In aª (A)

A:

Q: By using the e –- N definition of limits, prove пз — Зп - = 1. lim п00 п3 — п — 2

A:

Q: Recall that the Power Law states that for any positive integer n, lim [f(x)]" = ( li Apply the Power…

A: Topic  =Limits

Q: 1-cos 2x lim 4x

A:

Q: O 2x-12 fix)<x? for OLx3, Find lim flIN) <ーフ」

A:

Q: 2i (z-i) lim z?+1 1 - 1 1 O 2i

A: Consider limz→i2i(z-i)z2+1 = 2i(i-i)(i)2+1= 2i(i-i)-1+1= 00 Hence we will use L hospital's rule It…

Q: 8. )Prove that lim Vr = 2 using the e-8-definition. Hint: VI – 2 = x- 4 VI + 2 Puouo thot thoro…

A:

Q: 2) (9modoxT) I J16T I MAXI x2 a). Show that if |x +3|< 1, then 72√x +31. mod 2. Consider lim 2113 2…

A:

Q: Evaluate the following linits ) lim lim cos mn Cos nx

A:

Q: Let

A: We use definition to prove our result.

Q: 1.3 Evaluate lim using the laws of limits. 140 V1+ 3x – 1

A:

Q: Exercise 7. Evaluate lim vn(Vn+1- Vn). n00

A:

Q: Q) Find the limit of the following 1 lim 1+ Cos–

A: Given: limx→∞1+cos 1x To Find: The value of the given limit

Q: 8. Find the following limit. t+1 a) lim < t- +o 3t2 + 2 b) lim (ti- 3j + VE k) t 2

A: The solution is given as

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: