4. Use the e, 8 definition to show that lim,- (4x + 5) = 9.

Q: 1. Compute lim. ( ). 1 x→2+ 2 x² – 2x. where c is a real number. You may need to discuss according…

A: limx→2+1x−2−cx2−2x

Q: Use the fact that lim,ex = c and the result of Exercise 2 to show that lim,c X" = c" for any integer…

A: If the function is a simple function, the substitution of the point of limit into the function helps…

Q: Find the limits in Exercise

A: To evaluate: limx→5-3x2x+10 Solution: limx→5-3x2x+10 On simplifying further we get:…

Q: find the limit or explain why it does not exist. lim In (t – 3)

A: limt->3+ln(t-3)

Q: show that : Lim h→0  h / √5h + 4 − 2 =4/5

A:

Q: - Find the limit lim Xo 2x-3

A:

Q: Prove that lim, = 1, (x > 0).

A:

Q: 5. lim x-0 e2x-1

A: LetL=limx→ 0xe2x-1Plug in the value x=0L=0e2(0)-1L=01-1L=00Therefore Apply L Hospital ruleL=limx→…

Q: Find the limt lim e - x メ→の e-メ

A: Evaluate the limit  limx→∞ ex-x2ex-x

Q: Show that lim,→»(1+ e* for any x > 0.

A: To prove:

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

A:

Q: a) lim 2x e* +In x = ?

A: To find: The value of limit limx→+∞e3x+ln xe2x+x2. Concept used: Properties of limit:…

Q: ,3 Find lim (x,y)→(0,0) x² + y² °

A:

Q: It is known that lim-0 eAt-0 for A What can you say about e? Justify.

A:

Q: If lim, » 1512i (z2 + 30z) = x + iy, what is the value of a

A:

Q: 1 Ask for the answer to limx(1– e* ).

A:

Q: Use the precise definition (i.e. the ɛ, d definition) to prove that lim, →1 x2 – 3x + 5 = 3

A:

Q: If ƒ(1) = 5, must limxS1 ƒ(x) exist? If it does, then must limxS1 ƒ(x) = 5? Can we conclude anything…

A: A function f(x) is said to be continuous at a point x = a, in its domain if the following three…

Q: If A = lim ("C " C " C_ " C ……." C )m(a+1) then A² is equal to

A:

Q: Use the results of Section 2.3 to evaluate the limit lim e3×(x² – 6) =

A: Given that limx→0e3xx2-6 evaluate the limit

Q: if f(5) = 4, f'(5) = 7, then lim of (f(x²+1) -4)/(x²-4) = ?? when x goes to 2

A: Please see the answer below.

Q: Use the e-d definition to show that lim /a = 2. a-b (Hint: Vā – V6 =

A:

Q: For which value of c does lim -3 exist? You Answered 3 Correct Answer O None of the given choices

A:

Q: Determine the limit 2x z 3 lim,> 3z2 1 8x |5 O x=2/3 O x=-5/2 O x=-2/3 O None of the Above

A:

Q: (7) ifa lim has a point that the equalio- prove PCz,y) is above L and only if 3x +2y >4

A:

Q: Find the limit. lim (el – 1)* = 18x

A:

Q: The value of lim (trorozac) 2 (1² 1px (ozoz-ozoz) 6202 (17073— 170741) 7 is equal to

A: The property of exponents is anam=an-m. The property of exponents when the exponents are in…

Q: find the limit or explain why it does not exist. lim 12 In (2 – Vi) -

A: We have to evaluate the following limit: limt→1t2ln2-t

Q: e) Finally, prove that lim az-2 does not exist.

A: Use left hand limit and right hand limit to proof it

Q: Use the e-8 definition to show that lim VI = 2. Z-14

A:

Q: 6. Use the e, 8 definition to show that lim,2 x + 1 x+ 3 emlin

A:

Q: For which value of n, does the lim- -ny'+16n = 2 y-2 32-ys

A:

Q: Show that In x = 1. T bae amdinegoltox-1xlq ordt lim

A:

Q: Use the results of Section 2.3 to evaluate the limit lim e5x(x2 – 10) =

A: By product law,  limx→afx×gx=limx→afx×limx→agx

Q: Find the limit, if it exists. If it doe 3a + 3x + 4 lim 202 + Enter your an Enter DNE fo

A: We have to find  the limit .

Q: 1 Ask for the answer to lim x (1 – e * ).

A:

Q: 10. lim 2-と is A. -1

A: we have to find the value of the given  limit  lim    x→-∞2-x2x

Q: Compute the following limits exactly. 5* -7x +11 (a) lim x3+3x-4 X2 X TIX (b) lim 13sin(-A)-/24x +17…

A: Consider the limits a)limx→25x−7x+11x3+3x−4b)limx→613sinπx4−24x+17

Q: Is it possible to find numbers a, b and c so that an lim n+0o bn3 + cn erists but not equal to 0?…

A: Consider the function:

Q: Find the limit. lim In(x² – 1)

A: Given,

Q: Compute the indicated limit. „2 x + 3 lim x00 x - 4

A:

Q: Use the definition of the limit (e - 6) to show that 1 lim

A: By the definition of limit of a function, for every ε>0 there is a δ>0 such that fx-fx0<ε…

Q: Prove, using the formal definition, that lim,→1- V1– x = 0.

A: Given, limx→1-1-x=0

Q: Show that there is no number which satisfies the definition for the statement lim (-1)"+1 = a.

A: It is known that as n approaches ∞, -1n either gives the value 1 or -1.

Q: Evaluate lim,0+ e(1/z) .

A:

Q: ƒ (₂) If lim fx x-0 = L then which of the following must be true?

A:

Q: Find the relationship between e and s needed to prove S=

A:

Q: Find the shown limit.

A: To Determine:  find the limit. Given: we have limx→511x-3x2+1 Explanation: we have a limit…