Suppose that lim, ,-2 P(x) = 4, lim,,-2 M(x) = 0, and lim, „-2 s(x) : = -3, Find a. lim (p(x) + r(x) + s(x)) b. lim p(x) · r(x) · s(x) c. _lim (-4p(x) + 5r(x))/s(x) I--2

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

A: Given limx→0e3x-3x-14x2

Q: 1 Find lim +3 using limit rules. 2.

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Q: If -x2 - x + 1 ≤ g(x) ≤ x2 - x + 1 for all x does not =0. What is the lim x-----> g(x)?

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Q: (2x-1)(3-x) is (x-1)(x+3) limx→0

A: Given problem is :

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

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Q: find the limit of  limx->-4 [(x2-2x-24)/(x+4)]

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Q: If lim f(x)=-2 x-->0+, lim f(x)=3 x-->0-, and f(0)=-2, what can you say about lim f(x) x-->0?

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Q: iz2-z- lim- z²-1 z-a

A: We have to use polar substitution.

Q: V2x + 10 + Vx² – 5x + 10 lim - X→-1 x² + 1

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Q: 10 Find lim x12s 3. X->- X -25 2 lim Jx +3 - 2 メ→」 O lim Sitx - -x 3. 1-X 2 X

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Q: 1. Find a) lim x3 3-x b) lim- x3* 3-x ,c) lim- x+3 3-x

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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…

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Q: In(x-2) 1- Find , limx→2 In(x² -4)

A: Answer and explanation is given below...

Q: Determine the infinite limit limx→2− x^2 − 2x/ x^2 − 4x + 4

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

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Q: 2х — х +3 compute lim- x>* x² - 2x +5

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Q: calculate the limit limx→0  x3-3x2+x-5

A: To evaluate , limx→0 x3-3x2+x-5

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 -…

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Q: Once you know lim x-->a+ f(x)  and lim x-->a-  ƒ(x) at an interior point of the domain of ƒ,…

A: If we know the right and left-hand limit of a point then we know the limit at that point.

Q: lim In (x°) x2

A: We have to evaluate the given limit.

Q: Find the limit.

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Q: Find the limits

A: To evaluate the limit: lim1x2-4 (a). When x→2+. Evaluating the limit. limx→2+1x2-4=12+2-4=10+=∞…

Q: compute: Lim x2 + 12x -5 (x->1) Lim x+2/x2-4.    (x->1) Lim x2-9/x2-x-6 (x->3)

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Q: х2—1 lim х-1+ In(x)

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Q: Find lim *2 x -2 In(x- 1) by using the La'Hospital Rule.

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Q: 12-x-x 1- Prove that lim -7 %3D x-3 V6+x-3

A: our objective is to find the limit

Q: Let ƒ(x) = (x2 - 1)/( | x| - 1). Make tables of the values of ƒ at values of x that approach c = -1…

A: Make tables of the values of ƒ at values of x .

Q: Show that lim -e-* = 0

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Q: In(x-2) 1- Find , limx→2 In(x²-4)

A: The given limit is, limx→2ln(x-2)ln(x2-4)

Q: If lim f(x) =5 x-->1- and lim f(x)=5 x-->1+, what can you say about lim f(x) x-->1? What can you say…

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Q: √2+x-√2-x X lim- --0

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Q: Estimate the limit numerically for lim X4 x²-3x-4 4 3.9 3.99 3.999 4.001 4.01 4.1 X. x - 4 Lx2 - 3x…

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

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Q: • Find the limits of 2+x-V2 • lim Vx -3 • lim X→9 x-9 x³+1 lim X--1 x+1 V5+x -V5-x • lim x-0…

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Q: Evaluate the limit 6| lim x→6 x - 6. If the limit does not exist enter DNE. Limit =

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Q: Prove that lim -- (x + 1)

A: we have to prove that: limx→-1-5x+13=-∞   L.H.S:…

Q: Show that lim- e +1 does not exist. 1/x

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Q: To determine To find: The value of lim ( - →5 12-41-5 6(1-5)

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

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Q: Find the limit.  lim x--> infinity  ln (3x2-1/x2+1)

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Q: 2. If lim x, = 1 and lim yn = 0, then it is possible to formally prove that lim(x, – Yn) = 1.

A: (Solving the 2nd question as per our guidelines) Solution of 2: The statement is "If lim xn=1 and…

Q: Evaluate the limit 5 + 2x lim 8 – 8x x → 0

A: We haven the function is: f(x) = (5 + 2x)/(8 - 8x)  Dividing the numerator and the denominator by x…

Q: 9. Find the indicated limit. lim (6x - 21)³ x-4 = Show any work necessary

A: Solution: As per given data   lim( x tens to 4){ (6x - 21)³} As per simple rule of limit go ahead…

Q: Find the limit or show that the limit does not exist. lim→-0 4x2 + 3x + 2x x→-∞

A: See the details solution in below

Q: Use basic techniques to find the limits. 8. lim(-7) X-3 9. lim (x³ + 2x) X→-1 10. lim cos x

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Q: 3-Vx2+9 Without using L'Hopital's rule, find: lim-

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Q: a) calculate the limit x--> -7 x^2+6x-7/x+7 without using L Hoputals rule    b) calculate lim x-->…

A: Given: calculate

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

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

Q: 5) Find the indicated limit if it exist. а) lim X-2 3- Vx+ 7 2 - x x' +1 b) lim x-- x+1

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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:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.