Final Value Theorem:- 6, lim xin) lim xCt) ヒ→ lim (1-z) Xcz) (火(00)に

Q: What is lim x=inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^(3n)] + 2? (express answer as x,y)

A: Solve the following

Q: Evaluate using Theorem as necessary.

A: Given : The limit is limt→0 sin2tt .

Q: 5 tan(4x) x→0 3 sin(2x) Evaluate lim using L’Hôpital's rule.

A: The  L'Hopital's rule is: Suppose, f(x) and g(x) are two functions and their limit is given as:…

Q: What is lim m→0 sin(m) m ?

A:

Q: 2.2 a) Prove that lim,-2(x +2x – 7) = 1 using the e- ô definition of a limit. b) Find lim,-2 arccos…

A:

Q: To compute lim,_30+ (sinx) (In x), first re-write in which form? sin æ A. lim,0* īn z In a B. lim,0'…

A: Given that: 1. f'' at critical points.2. limx→0+(sinx)(ln x)

Q: Find the limit. Enter the exact answer. lim sec 3x cos 7x = x

A: I am attaching image so that you understand each and every step.

Q: lim cos x+4e* is 5er

A:

Q: 3n Find lim„→∞ (1+)" . Hint: Apply L'Hopital's rule.

A: Please refer the attached image for complete solution.

Q: x + tan x 2? — 5х — 14 - (а) lim x0 3x + 4x² (b) lim (Do not use L’Hospital rule in part(b)) x7- x2…

A: Using rules of limit's.

Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2? (express answer as x,y)

A:

Q: b) If x sin x 2 - 2 cos x hold for all values of x close to zero. Find limx0 xsinx ? 2-2cosx

A: Given, limx→0xsinx2-2cosx

Q: Evaluate: lim, (cos z). Show your solution. O -1

A: Limit of a function f(x) at point x = a exists only when Left hand Limit(LHL) = Right hand limit…

Q: 5. Use L'H rule to find (a). lim Inz2 (b). lim (sin x)(In x).

A:

Q: 9. Build a table to estimate lim sin - (Hint: Use multiples of T) (x³ - 3x2 + 6– 2x) 10. Use a table…

A:

Q: (c) Prove the value of lim Sin 3a o Cos 4Do NOT use L'Hospital's Rule.

A: The given limit is,

Q: 3.lf limT(x--1) [(x^3+x^2-ax)] =1-a, then a= O a. 1. O b. 0. C. -1. O d. 1/2. 4-The equation…

A:

Q: Show that lim [x2 sin (1/x)] = 0.

A: Given: limx→0x2sin1x

Q: lim,-o ([sin x]*) is

A:

Q: Use the Squeeze Theorem to show that lim (x2 sin(2)) = 0 x-0 %3D

A:

Q: 1. Use L'Hopital's Rule to calculate the following limits: (a) lim- sin . (b) lim,1- T/2-sin-la…

A:

Q: Exercise 3: Use the squeeze theorem to prove lim0 sin(x-1) = 0

A: To prove:

Q: (a) Show that tan x = sec?x using quotient rule. dx x+8 (b) Find lim X-2 x+2

A: Solution-

Q: Find values of a and b such that sin 3x + ax + bx³ lim = 0 x3

A:

Q: Q \ Find the value of 8 > 0 that guarantee lim x-0 csc(1/x) = 0 in terms of ɛ?

A: Definition of limit: We know that, limx→af(x)=L               ...(i) For each ϵ>0, there exists a…

Q: 2t – 1 Evaluate lim,, tan-1, e> - t - 1

A:

Q: Q. Prove that: Lim tanhx =1 .

A:

Q: . Does knowing that | sin (1/x)| < 1 tell you anything about lim (x,y)→(0,0) y sin -?

A: To find the limit of the problem

Q: Find the Oimits :- sin 3y Lim Sin Jz8 Lim My JzO ot

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

Q: tan t sec 2t 2- lim 3t

A: Using rules of limits to find the answer.

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: (a) lim x→0+ (sina) 1 (b)…

A: Given: (a) limx→0+sin xx1x2            (b) limx→01sin2 x-1x2 To find: Evaluate using L'Hospital…

Q: lim (In(x))* ?

A:

Q: What is the lim, 0+ sin(y) In(y)?

A: limy→ 0+sinylny=limy→ 0+lny1sinyBy L'Hopital's rule,=limy→ 0+1y-cotycscy=limy→…

Q: 3. Use Squeeze Theorem to evaluate lim 1-0+ sin(In r) In(sin æ)"

A:

Q: 30. Use the fact that lim x→0 sin x X = 1 (shown in video) to show lim x-0 1 - cos x X = 0

A: we will find the required.

Q: Evaluate limt--&gt;0(tan 4t)/(t sec t) Without using L'Hospital's rule.

A: To calculate the required limit without using the indeterminate form

Q: 2. If lim x, = 1 and lim yn = 0, then it is possible to formally prove that lim(x, – Yn) = 1.

A: (Solving the 2nd question as per our guidelines) Solution of 2: The statement is "If lim xn=1 and…

Q: 5. Prove that if lim g(r) = 0 then lim g(x) sin () = 0. %3D

A:

Q: Show that lim (x,y) → (0,0) 12 √16x +9y¹ 4x²+3y does not exist. Please show a complete solution.

A:

Q: Why does lim sec x = – o? How is this related the triangle in the drawing below? Explain. Adjacent

A:

Q: (b) Consider lim tan(4z). -7z What does the numerator approach as z- 0 ? What does the denominator…

A:

Q: 1 Prove that lim dx exists and find its value. (1+x?)" 1/2

A:

Q: By using Sandwich Theorem, prove that lim sin x

A:

Q: Evaluate the limit. 3 sin? 2x lim х—0 8x2

A:

Q: Evaluate using Theorem 2 as necessary.

A: Given: limx→0 x2sin2(x)

Q: 3+2r lim エ→0 =?

A: Given , limx→03x2+2xx

Q: Let a > 0 be a real number. Prove that lim x“ sin = 0.

A:

Q: 1 x |=? Use L'Hospital's Rule 4 lim- 5 arctan -4 arctan 5 xVx

A:

Q: Q show that lim %3D メ→ 0-1

A: We have to show that limx→0.11x=10 L.H.S : limx→0.11x           =10.1               (plug in the…