a) Evaluate:- 1: lim (xcot x) I-V31 + 4 2: lim 4-1 3: lim $(x-5)

Q: 5. a) Explain why lim vx-3 does not exist. b) What about lim V(x 3)2 ?

A:

Q: lim (x3 +x

A:

Q: Compute:

A: Given: limx→6 f(x)=4

Q: Suppose that lim f(x) = 3 and lim g(x) = 5. Then lim g(x). %3D %3D X2 X2

A: Given: limx→2fx=3 and limx→2gx=5. To find: limx→2fxgx2+2fxgx Solution: Product rule of limit states…

Q: What is lim 2 (x - 2)

A: Given

Q: What is lim In x? x→2

A:

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

A:

Q: The value of lim (xe- x) will be ...

A: It is given that limx→∞xe-1-x.

Q: lim .2 X → 00 et?

A: Given query is to find the limit of the expression.

Q: ,3 Find lim (x,y)→(0,0) x² + y² °

A:

Q: х-V4х+5 1. lim х-5 х2-25 1 4 2. lim х--з+ \x2+3х-18 7x2-11х-30,

A:

Q: Compute

A: The limit of the function is the value of the function when the value of the arguement is…

Q: Evaluate the limit. 3 1 lim -1-\2x² + x –1 x + 1/

A: limx→-132x2+x-1+1x+1

Q: Which property of f(x) = x' allows us to conclude that lim x = 8? x+2

A: f(x) =x3

Q: Prove that lim x 2 = 4. x→ 2

A:

Q: メ-D4 xー12 In do torminate Form Lim | १ - 3

A: Given:   Limit equation is given

Q: Using the ɛ, & definition, prove that lim V = 1. %3D x 1

A: We have to prove the given limit.

Q: What is the definition of lim f(x)?

A:

Q: lim (3x + 5) = 2, x→-1

A:

Q: Evaluate using substitution.

A: limx→-π23sin x

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: Evaluate the following limits. х* + 3х + 2 lim, 'x-1 v2 x² + 4x +3 a. x² – 2x lim, „2' Vx² +5- 3 b.

A:

Q: True or false? if lim fcx) exists but Lim gx) does DぐX not exist, then lim. fox)+gox)) does…

A:

Q: Find the following 1 х — 6 lim 2-4- 4 b lim r-3 27 - r a lim -6 (x – 6)6

A: We have to use l hospitals rule to find limits

Q: Evaluate the indicated limits 3z – 5z² + 7 (i) lim 1-400 8+ 2x – 5x4 lim

A: To find: limit of the given function

Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find lim x→ -2 (-4p(x) +…

A: Given limx→-2p(x)=-4 , limx→-2r(x)=0 and limx→-2s(x)=-3We need to find:limx→-2-4p(x)+5r(x)s(x)

Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find lim x→ -2 (p(x) +…

A: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find limx→ -2(p(x) + r(x)…

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: 3x lim x→∞ √x²+1

A: We can evaluate the limit as below.

Q: 4) lim,-16 () x²-256 4-Vx

A: using the property  a2-b2 =(a-b)(a+b)

Q: Evaluate Lim マ-1 X-1 区 -1

A:

Q: 2.) Evaluate the one-side d limitss lim Jx+7 = メラー7 lim xキ7 - メーマー7+

A:

Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find x→ -2 p(x). r(x) .…

A: Suppose that limx→-2p(x) = 4, limx→-2r(x) =0, and limx→-2s(x) =-3.

Q: 2) lim X+1-x1 メーーt メーー 2x+2

A:

Q: 4. Use the &, 8 definition to prove that lim (4x-1) = -9.

A:

Q: Evaluate the limit. 4 lim + 2 (x + 3)? x → – 3

A: Consider the given limit, limx→-3-4x+32+2 now, apply the rule of the limit that is the limit of a…

Q: Determine limx→−2 6/x-2, if it exists

A: limx→−2 6/x-2 yes limit exist and we can direct apply the limit so put -2 in given function…

Q: Evaluate the following limits: -5x - e* Lim -40 12 sin x i. lim x → 00 ii. x-4,

A: We are given two limits to evaluate.  Both of them are of inderminate forms.

Q: By using the e- & definition, show that lim 2² + X 4 = 1.

A: By the €-δ definition of limit,

Q: Evaluate the limit. 8x 4 lim x→4 \x² – 16 X -4,

A: To evaluate the limit: limx→48xx2-16-4x-4 Solution: We can find that if we evaluate limit then we…

Q: What is lim (x? – 4x + 5)? O 1 O 2 O does not exist

A: To find÷limx→2 x2-4x+5    limx→2 x2-4x+5=22-42+5                           =4-8+5…

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

A:

Q: Part I-Evaluate the Following Limits: 1. lim 5 X-1 2. lim (- + 2x+ 4) X-1

A: topic - limits

Q: Q1: b: Evaluate the limit: (1) lim-11 17-1 x-1 -2x-4 (2) lim,--23+2x² sin(x-3) (3) lim,-3²-9

A:

Q: 2. Letgx-15x+2,-2,x+2, x0. Does the limx - Og(x) exist? If yes, give its value. If not, why?

A:

Q: State the precise definition of lim f1x2 = L. xSa

A: State precise definition of limx→afx=L

Q: Find the limit or show that it does not exist lim 212 + 3t – 5

A:

Q: State whether lim f (x) and f(c) are equal or unequal at the given value of c. Also, state whether…

A: Since you have posted many questions here, I can answer only first 3 subparts at a time. Please…

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.