(1) Evaluate the limit, if it exists. (a) x² + x - 2 lim t→1 x² - 4.x + 3 (b) x - 81 lim x→81 Vx - 9

Q: Find limit of lim x-->0 of f(x)= (e3x-3x-1)/(4x^2

A: Given limx→0e3x-3x-14x2

Q: 1- Find the limits: lim V - 1 メ→ x-1 а. 2x3 b. lim x- 00 3(x-2)2 2x3 c. lim x2 3(x-2)2 x+1 d. lim…

A: Consider the limits  a.limx→1x−1x−1b.limx→∞2x33x−22c.limx→22x33x−22d.limx→3x+13−x2

Q: lim x 1. x- 3.

A: Follow the procedure given below.

Q: Find the limit V3x(x-1) lim→1 |x-1|

A: we have limx→1-3x(x-1)|x-1| this is 00 indeterminate term

Q: See pencil for correction of problem

A: First we simplify the expression (x2-2x-8)/(x+2)=(x2-4x+2x-8)/(x+2)…

Q: B. Find the value of the limit. 1. lim *+1)²(x-1) x1 x³+1 x²–4 2. lim x1 x2-3x+2 x²-4 3. lim x2 x-2

A:

Q: 2. Use the definition of the appropriate limit to show (a) limr→∞(2x² + 4x – 1)/(3r³ + 1) 0. - (b)…

A:

Q: x² – 1 lim x→1 x – 1

A:

Q: B. Find the limit. Зх— 1 5. lim х-1/3 9х2-1 x3- 1 6. lim х+1 х-1 Vx+5 -2 7. lim X→-1 х+1 Vx-1 4. lim…

A:

Q: x2 + x -6 2. Use the precise definition of a limit to prove lim2 x - 2

A:

Q: Determine the limit at infinity. 4 22) lim 9 - (5/x²) X→-0

A: step 2 complete solution

Q: 3. Determine the infinite limit. x² + 3x lim x--1- x2 + 2x + 1

A:

Q: The value of the limit x42x-3 lim メー)イ X-イ

A: Given : limx→1x2+2x-3x-1

Q: Evaluate the limit: -V4+x² lim X→0- x2

A: limx→0--4+x2x2

Q: Find the limit. . lim 2x²-x-3 X-1 x+1 . lim 2+h-vZ x-5 E lim x-5+ x2-25 . lim o. f (x) = fx³ +3 lx -…

A:

Q: V2x -1 Using defination of limits, prove that lim Jx- 3 L^ = x4

A:

Q: x- 2 x <4 Estimate lim Ax) where fx) = %3D x+2 x24 12 10 -8- 8. 6 2 Limit does not exist.

A: Check the value of function nearer to given point of limit if they are equal only then limit will…

Q: Find the limits of x² 1- lim Vx+1 -1 +x - 6 2- lim | x+3 x→-3

A:

Q: (-5-x)²+2 if x #-6 Let f(x) = 2x + 14 if x = -6 Calculate the following limits. Enter "DNE" if the…

A: Given  f(x) = -5-x2+2if  x≠-62x+14if  x=-6

Q: 4-VE Find the limit: lim→16 x-16

A: We need to evaluate the following limit limx→164-xx-16

Q: What is lim )-7(0) if f(x) = 2x2 + 1? x-0 The limit does not exist. 1

A: Solve for the limit

Q: 2+4x 7. Prove lim = 2 using the e-ô definition of the limit. 3 %3D X-1

A: Hey, since there are multiple questions posted, we will answer first question of the first image. If…

Q: 10. Evaluate the limit: -3x -9 x +3 lim x--3+ \x2 +x- 6 x-2/

A: Given: L=limx→-3+-3x-9x2+x-6+x+3x-2 We know that  limx→afx+gx=limx→afx+limx→agx…

Q: 4. The graph of a function f(x) is shown at right. If g(x) = V1+ 3x , find lim [f(x) + 3 g(x)]. %3D…

A: The graph of the function fx is given. From that graph it is clear that, the function fx, at x=1…

Q: 2 – 5x – 14 Evaluate the limit: lim - - x - 2 x + 2

A: Topic:- Limits Answer =  -9

Q: Use lim f(x) = -2 and lim g(x) = 5 to find the limit. %3D lim [3f(x) – 4g(x)]

A: The given limits are limx→cf(x)=-2 and limx→cg(x)=5

Q: Determine the infinite limit. x² - 4.x lim 1+4+ x2 - 8r + 16

A:

Q: Find the constant c so that the limit limx->3 (x2+x+c)/(x2-5x+6) exists.

A:

Q: Evaluate the limit. 4x2-9 lim x→3/2 15-10x а. b. lim(x – 2) sec(n/x) | x-2

A: See the details solution in below

Q: Find the limit. (a) lim x→3 Vx +6 – x x3 – 3x2

A:

Q: 4-V3x+1 Evaluate the limit limx→5 x²-7x+10

A: Given limitlimx→5 4-3x+1x2-7x+10

Q: 1. Find the limit. x² - 25 lim x 5 x² - 8x + 15 ૨૨

A:

Q: (3) Find the limit. 1- x lim 1+3- X – 3

A:

Q: 1- Find the limits: Vx- 1 lim xI x-1 а. 2x3 b. lim X- o 3(x-2)2 2x3 c. lim X-2 3(x-2)2 x+1 d. lim…

A: Given: a)  limx→1x−1x−1=?b)  limx→∞2x33(x−2)2=?c)  limx→22x33(x−2)2=?d)  limx→3x+1(3−x)2=?

Q: 2. Find the limit of the function (if exists). If the limit does not exist, explain why. For…

A: (b).   limx→0 x2+a2-ax2 ;      a&gt;0

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞  5x2…

A: The given limit of expression is lim x→∞+5x2+5x-42x2-3x Divide the expression by highest denominator…

Q: 18 -a+1 Find the limit lim a9 2x2+3x-1

A: Given, limx→918x2-x+12x2+3x-1   To evaluate limit

Q: .7 Find the limit: lim .3 1 - x→1 x³ – 1 - 1

A:

Q: 3x + 2 aluate the limit of lim if it exists. x + 2 O limit does not exist

A:

Q: 44. Prove that if lim f(x)= L #0 and lim g(x)= 0, then the limit lim 8(x) does not exist.

A: Given: limx→cf(x)=L≠0 and limx→cg(x)=0 To Show- limx→cf(x)g(x) doesnot exist. Theorem- if limx→au(x)…

Q: V5x+6-4 1. Use L'Hopital's rule to evaluate the limit: lim- x-2

A:

Q: Find the limit if it exists. If the limit does not exist, explain why. (x+h)³-x³ C. lim. h-0 h |x+4|…

A:

Q: 2/ Find the limit of the function lim X415 хъ Ч 2 X

A:

Q: 6 Find the value of a such that 2x2 - ах — 14 lim х-1 х2 — 2х — 3 exists, What is the value of the…

A: The limit of a function at a point 'a' in its domain is the value that the function approaches as…

Q: 5. Find the limit of lim x* +0-x

A: Topic = Limits

Q: |x| does not exist. Show that the limit lim x 0 X

A: Given: limx→0xx

Q: Find the limit. lim(v² + x = x) = lim( Vx2 + x – x

A:

Q: Prove that the limit does not exist. |x – 6| lim x 6 X - 6 SOLUTION 19 – x| X - 6 lim lim x → 6+ X -…

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Q: Use numerical evidence to estimate the value of the limit to at least 2 decimal places. x² + 2x - 48…

A: Solution:

Q: x² – x + 1 1 - (c) lim x→1 x + 1 2 using definition of the functional limit

A: We can prove the statement as below using definition of limit