-e g). lim [In(6x² + 5) – In(3x² – 6)] h). lim ズ→の

Q: Evaluate the limit. 2² 4x+3 lim,>∞ 3x³ - 2x+3 01 O 1/3 0:3

A: Given: limx→∞ x2-4x+33x3-2x+3  To find: Value of the limit.

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: Prove rigorously that lim (4 + 8x) = -4. X-1

A:

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: can this be evalnated by using L'HOSpital's Ruie? lim Trxln(x) Itxen(x) (メ-)nx

A: The given limit can we evaluated by using algebra of limits.

Q: Suppose lim f1x2 xSa o and lim glx2 = ". Prove that xSa %3D lim 1f1x2 + glx22 xSa

A:

Q: Given that2x – 6 <g(x) <x² – 2x-3, use the Sandwich Theorem to determine lim g(x). X→3

A:

Q: 2) Calculate lim ( In(3x + 1) – In(2x + 1)). -

A: Since you have asked multiple questions, we will solve the first question i.e., Question-(2) for…

Q: The value of the limit 2-x3 lim x2+3x3 is Select one: -1/3

A: The given expression is limx→∞2-x3x2+3x3

Q: . Let P(r) = 5x³ – 3rª + 3x³ − 9r + 5. Give a step-by-step € – 8 proof that - - lim P(x) = P(1). I→1

A:

Q: Find the limits in Exercise

A: Given limx→∞x-34x2+25.

Q: Show that |x2-4|&lt;e ,  when 0&lt;|x-2|&lt;e(5+e)-1 and prove limx-&gt;2 x2=4 by using these…

A: Note: The statement is verified by the ϵ-δ statement of limit.

Q: 1. Prove lim, n+2n³+7 2 0, using the definition.

A: I have used only definition of limit of sequence

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

A: We have to find the lim inf and lim sup of sequence

Q: Find the lim inf (xn) and lim sup (xn) of Xn=3-(-1)"

A:

Q: Prove that lim X-2 2x2-3x-2 = 5. x-2

A: Topic = Limits The given equation is limx→22x2-3x-2x-2=5

Q: Use the e-N definition of limits to show that 2n -15 lim = 1. %3D n0o 2n - 13

A: The objective to show that limn→∞2n-152n-13=1.

Q: 1 When demonstrating that lim x → - 0.5 4x + 2 with M 1000, which of the following &-values…

A: For the expression limx→-0.514x+2=∞ with M=1000 The objective is to find the value of δ.

Q: Prove that lim(4x² – 25) = -9 X-2

A:

Q: Use the definition to show that 4n – 5 lim 2n + 3 - 2. n00 3.

A:

Q: Evaluate the limit 6x 2x 9x lim 3x 9x 3

A:

Q: Find the limits in Exercise

A: Given,          limx→-1416x13x+162

Q: Prove that lim x 2 = 4. x→ 2

A:

Q: 6-2x Prove by definition that lim 4. 3

A:

Q: 5. Prove that lim Show your t→-2 t+2 complete solution.

A:

Q: (a) Show that lim Vr2 + 4x + 3 – x = 2.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: You are not allowed to use L'Hospital's Rule 2x2 – 32 - lim V3x + 4

A:

Q: Prove rigorously that lim (4 + 8x) = −4. x→−1

A:

Q: Pip wants to complete the track shown below but, because there is lim- ited space, additional plates…

A: We will use the basic knowledge of shapes and patterns to answer this question correctly and…

Q: Find follewing lemits x3-14x3+ lim 42x+2 b-X Answer 'as an in teger. orwholenember

A: Find the limit of the function (x3-14x2+42x+2)/(x-9) as x tends to 9.

Q: Prove that lim [V4n² + n – 2n] = -

A: Use rationalize to solve

Q: 7x2 lim Does not exist

A: To Determine: find the limit  Given: we have limx→07x2x2 Explanation: we have limit limx→07x2x2 let…

Q: Prove that lim(4x2 – 25) = -9 x-2

A: First we use the formula a2-b2=(a-b)(a+b) then put the limit.

Q: Suppose that the lim x2 flx)- Which of the follomng State ment cannot be true ?

A: We have to find which of the following statement can't be true.

Q: Evaluate the limit 7x2 2.0 2x +3 lim 3x +4

A:

Q: Evaluate the limit: lim 7t - 3t = %3D t 2

A: Limit. Limit of a function at a point if the value of the function at the point or the value of the…

Q: Find the limit.

A: To evaluate the limit:limx→2xx2+1 Evaluating the limit. limx→2xx2+1=222+1=24+1=25

Q: Let –2x2 + 8x – 11 < f(x) < 2x² – 8x + 5. By using sandwich theorem, find lim f (x). x-2

A:

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

A:

Q: Prove that lim r = 2 using the e-8-definition. Hint: VI - 2 = VT + 2

A:

Q: Find the limit: (a) lim 3x+9x2-4x+17 5x3-3x-14

A:

Q: The infinity in the V6-ydy can be eliminated by applying lim t+ - True False

A:

Q: 2) G VALUATE THE UMIT, IF IT EXISTS. Lim X-3 x2-X-12 uT x²+ 3x 2)

A: Given:         limx→-3x2+3xx2-x-12   Factoring                   =limx→-3xx+3x-4x+3

Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim(5x + 2) = 17x➔3

A:

Q: Compute the indicated limit. 5x? – 5x – 3 lim 3x3 – 5x 7

A:

Q: The value of the constant k such that x²– kx+6 lim exits is X→1 х—1 б -6 -7 7 -8 8.

A: 1). From the given problem:   fx=2x+14   From the power law:   dxndx=nxn-1.   So,…

Q: In (3t) lim t2

A: Given : f(t) = ln(3t)/t² To find : Limit of the function

Q: Given that f(x)={kx2+2,≤22kx,x>2. If limx→2f(x) exist, then k equals.

A:

Q: Use e-5 definition and prove that lim (2 5r) -6

A: Here we use basic definition of epsilon and delta .

Q: 7. Evaluate the limit: 9x2 -2 lim 2 3x 2 x-3

A: To evaluate the limit:limx→239x2-22-3x Solution: It is 00 form. We will use L-hospital rule. In…