37. Prove that lim Vx Hint: Use Vx - e

Q: х3 + 6x2 — 32 – 32 1. lim х--4 х3 + 5х2 + 4х

A:

Q: c) limx'e*

A: We apply L-hospital's Rule to find limit.

Q: Evaluate using the Squeeze Theorem.

A:

Q: tanh r 4. lim -40+ secha - 1

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: justify lim O Find and the xy

A: It belongs to Multivariate Calculus (specifically several variable),so I can do it in advanced…

Q: In z O lim

A: Please refer the attached image for complete Solution.

Q: x2 + 8x – 9 4. lim x→1 x3 2а? — 5х + 6 - -

A:

Q: Prove that lim r(x)= where m = 0, 1, 2, 3. .. II

A:

Q: 7. Use L'H rule to find (a). lim (- ), (b). lim rInz?

A:

Q: Prove the statement using the ε, ?  definition of a limit.

A:

Q: Q: Prove ha中 Lim x" an %3D

A: we have to prove that the following

Q: Compute the following limits.  limx->2 1/(x-2)5.

A:

Q: What is lim In x? x→2

A:

Q: 5. Use the precise definition of a limit to prove that: lim +23D3

A:

Q: Use the definition to prove that lim,→∞ x² = ∞.

A:

Q: 3. Use the precise definition of a limit to prove lim(9 – x) = 5

A:

Q: Use the definition of limit to show that lim x, = 0. Inn a) Let x,

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: Evaluate the limit. lim x² In x x→0+

A:

Q: Evaluate the limit using L'Hospital's rule 1 lim 3xe 3x

A:

Q: Prove that lim(x,y)→(1,2) (x2 + 2y) = 5 by using the precise definition

A: ε-δ definition: Limit of function f(x,y) at a point (a,b) is 'L' if for every ε>0 there exist…

Q: Prove that lim r(x) = 0 where m = 0, 1, 2, 3. ...

A:

Q: Prove limx→∞(1/x)=0

A:

Q: Prove that lim (r2- 1) = 3 using the e, 8 definition of the limit. %3D 141 Linh tL

A:

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

A:

Q: 2. Let r > 1. Prove that lim r" = 00,

A:

Q: Verify using the definition of limit (with e and 8) that lim (13r – 1| - 1) = -1, explaining all…

A: Formal definition of Limit. Let f be a function defined on an open interval containing c (except…

Q: Let a and b be positive real numbers. Evaluate lim (ax – Vax – bx) in terms of a and b.

A: To evaluate limx→∞ax-a2x2-bx where a and b are positive real number

Q: Find the limit. lim tan7x In2x = %3D

A: Solution..

Q: swer of the following lim 2x²+6y² lim (x,y)→(0,0) x²+y²

A:

Q: limy→6 Vx - /6 9, 3 '- (6)³

A: Given that:-limx→6x-6x3-63we know that the formula:a3-b3=(a-b)(a2+b2+ab)a2-b2=(a+b)(a-b)applying…

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

A:

Q: Find the limit. lim tan5x In2x = x→0+ %3D

A: Given :   limx→0+ tan5xln2x

Q: Prove that lim,→3 3x – 7 = 2 by using e, d definition of limit.

A:

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

A: Using squeeze theorem,

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

A:

Q: ve that lim 1 by definition.

A:

Q: lim(x, y) – (5,9)(÷ ) = ;

A: To show                limx, y→5, 9xy=59 using the epsilon-delta definition of limits. Pre-requisite…

Q: Calculate the limit limx→0cos3x−cosxx2.

A: To Determine: calculate the limit  Given: we have limx→0cos3x-cosx2 Explanation: we have a function…

Q: Compute this limit to infinity   limx→∞ of (7x^3 + 2020x+ 4)/(πx^3+ 18x^2+ 12)

A:

Q: Prove that lim (2x – 7) = 3 by using the e, 8 definition of a limit. x→5

A:

Q: If lim(x,) =5100, then (Xn) is bounded. Select one: O True O False

A: 1) Here, lim (xn)=5100 that is finite. That is the sequence xn is bounded. So, the statement is…

Q: The infinity in the V6-ydy can be eliminated by applying lim V6-y dy O True False

A:

Q: Use L'Hôpitals Rule to evaluate lim xln( 1+

A: If we have an indeterminate form 00,0∞,∞0,∞∞for a rational function f(x)g(x)then we have to apply…

Q: 4. Use the definition of a limit to prove that lim z = a* for any real number a.

A:

Q: use the squeeze/sandwich theorem to show that lim x-->0 (x^4cos(1/x)) = 0

A:

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

A:

Q: Prove using the def. Of a limit (b) limx→0(2x^2) − 3)) = −3

A:

Q: a2 +bt -a lim² , a >0 t-0 t

A: