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

Q: 42. Prove that if lim "O = 5, then lim h(t) = 15.

A: It is given that To prove that

Q: Evaluate the limit.

A: It is given that, limh→π21-cos3hh   It is known, that if we have limx→af(x)g(x) and after plugging…

Q: Estimate the limit numerically. ++7,000x³+ 800,000 lim 2x° + 1,269x³ 8. O to∞ 2.

A:

Q: Use l'Hôpital's rule to find the following limit. 3x-2x lim 3 X o 5x° +3

A: To use the L-Hospital rule to find  Lim(x tends to infinity) [3x³-2x]/[5x³+3]

Q: b* – 1 Show numerically that for b = 3 and b = 5, lim аppears to equal In 3 and In 5, respectively.

A: Given : limx→0bx−1x

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

A:

Q: (b) Show that if lim sn = +o∞ and lim tm > -x, then lim($n + tn) = +0.

A:

Q: Find the limit. lim sec x

A:

Q: 1 Use l'Hopital's rule to evaluate lim 1+0+ \I In(1 + x),

A: Question is solved.

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

A:

Q: 4 Find the limit lim 3 Enter I for oo, -I for -o, and DNE if the limit does not exist. Answer:

A:

Q: Use definiction to १r० v of Conkegene to lim n+4

A:

Q: lim 4 x→0 2 1 +sin (2) cos sin

A:

Q: S* 56sin(t")dt Evaluate the limit lim .8

A:

Q: 2. Use L'Hospital's rule to evaluate the following limit. cosh(3x) – 1 lim x→0 x2

A:

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

A:

Q: Evaluate the limit: lim sin(2x) cos(7x)

A: To evaluate: limx→0sin2xcos7xx

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: Suppose that a, > 0 and converges. lim na, = 0. Prove that Ea, n 00

A:

Q: 1. Show using sequences of functions that lim -nz? e dx 0.

A: Solution is below

Q: Compute the limit below. 3(In a)²+3(lnz)+2 lim (In a)²+1

A:

Q: 2x + 1 (a) lim 9x2+ x

A: We have to solve the limit

Q: Compute the following limits if they exist. secr - 1 (a) lim

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: We want to find the limit lim os(2æ) – cos(7x) - x2

A:

Q: Evaluate the limit: 1-Cos(9h) lim h h >0

A: Find the limit When we plug in 0 for h, the denominator becomes 0 So it is undefined.

Q: If x4 <=ƒ(x)<= x2 for x in [-1, 1] and x2<=ƒ(x) <= x4 for x <-1 and x> 1, at what…

A: Summarizing the given information:             . We need to find out that at what points c, we…

Q: 5. Use the definition of limit to prove that lim[(x – 1)(sin x²)] = 0

A:

Q: Evaluate the limit: lim sin(7x) cos(4x)

A:

Q: Use l'Hôpital's rule to find the following limit. 1 1 lim In (x- 2) X- 3 X→3 1 1 lim In (x- 2) x-3…

A: Consider the provided expression, limx→3+1lnx-2-1x-3 Find the limit of the provided expression using…

Q: (b). Compute each of the following limits. (i). lim,4 ". (ii). lim,0 tanz

A: For (i),     limx→ 4x2-x-12x2-4x=limx→ 4(x+3)(x-4)x(x-4)=limx→ 4x+3xPlug in the value x=4.=4+34=74

Q: Find the limit, If it exists. 8 lim 9 cos 5x

A:

Q: Find the limit, if it exists

A:

Q: sin(72) lim 2-16 In(z – 5)

A: find limz→6sin(πz)ln(z-5)

Q: Compute the indicated limits. sin(2x) lim 3x

A:

Q: 2. Compute the following limits: (a) lim -x+ 7x + 3 (b) lim -x* + 7x +3 3 + 7x + 3 (c) lim

A:

Q: use L'Hôpital's Rule to compute the limits: (1++)" (а) lim 2x. (b) lim (x tan r. 2.

A:

Q: (ii) 2tan?x lim- x2

A: Given that: limx→02tan2xx2

Q: Find the limit. lim ,2 x cos

A: limx→0x2cos1x = ?We know:   cosθ ∈ -1, 1

Q: Q3 (A): By using "L' Hopital rales "; Find the limits of: (1) tim-al-ca (2) lim, x(tan"¹x-x)

A:

Q: Examplesa using the definitin of limait to .2 2. Prove i lim Z =Z

A: In mathematics, a limit is the value that a function (or sequence) approaches as the input (or…

Q: 2. Use e -d of the limit to prove that lim z= 4

A: Given below the detailed solution

Q: sin r lim ,3 81.

A:

Q: Find the limit lim, n cos(x +x) / sec(x) + 5

A:

Q: Find the limit. lim ey sin P -(5, 0, -5) O 1

A:

Q: Find the limit of the following: lim In(3+ex)-In(9+x)

A: Use the properties of lograthim first than put the limit.

Q: Using the epsilon-delta criteria, our aim is to show that lim 3z – 2i = i. z→-i Which among the…

A:

Q: Evaluate lim S", r³dx . O 4 Does not exist.

A:

Q: 1. Use L'Hopitals's rule to find lim c In(e" – 1). |

A: limx→0+ xlnex-1