4) evaluate lim x-->2 (2x2 - x - 6) / (x2 - x - 2)

Q: is it true that ∇f(limx)=lim∇f(x) and further that ∇2f(limx)=lim∇2f(x)?

A: We know,  ∇f(xi)=f(xi)-f(xi-h), h=xi-x0i,i=0,1,2...And…

Q: 2-limx-o(x. secx.cscx)

A: To find the limit of the following.                                     limx→0 (x sec x csc x)

Q: How does the function behave as lim x → 3- for 7/(3(x-3)(5-x))?

A:

Q: Suppose that ƒ is an even function of x. Does knowing that lim x-->2- ƒ(x) = 7 tell you anything…

A:

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

A:

Q: Limx-->9 = X -9/ (X)1/2 -3

A: We will first cancel out the irrational factor at the denominator. And then we will check if the…

Q: Show that lim(5x+2)=-18 x-> -4

A:

Q: Evaluate the limit. 1 1 lim x--4X + 4

A:

Q: 4-x lim,.

A: The given limit is limx→∞4-xx

Q: Evaluate lim 2 X-2 x-2

A:

Q: 3. Explain why lim √2x - 6 does not exist.

A: 3. The given limit is limx→32x-6 Note:    Multiple questions are given, we are answer with only one…

Q: Find the lim x-->0 (x2-x)/(x2+x)

A: We have to find the limit                                      limx→0x2-xx2+x

Q: 8. Compute, justifying, lim5 x2 +9 - V2 x² + 9 )/ x² .

A:

Q: lim x---q -8x2 + 1/x2 + 1

A: To find the limit  limx→q-8x2+1x2+1

Q: Determine lim(3x - 5). x----2

A: To find: limx→2 (3x-5)

Q: lue of lim X→-4 2x+8 x²+2x-8* Remember to fully justify your.

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: х2-х-2 с. lim х>-1 х3-2x2—3х

A: (c) Given limit is : limx→-1x2-x-2x3-2x2-3x To determine the value of given limit.

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: 6. What is lim 1 -? Why? -40 In(x) 10 8 4 2- 5 6 10 -4 -8 -10 3- 2.

A: To find

Q: 2x lim x→9- 4-/25-x

A: This question is related to limits, we will solve it using given information.

Q: Find: lim --9 ,2_9x x2-9x x→9

A: We have to find value of  Limit x tends to 9  (x-9)/(x^2-9x)

Q: Lim 2x3 In x

A:

Q: lim (2x-5x) is x--2

A:

Q: Find lim 2-0 -x-1 x²

A:

Q: х-2 Determine lim x→2- 2-V4x-x²°

A:

Q: x³ - 125 lim x-5 x - 5

A:

Q: How to find  lim 4-x/x+3 while its approaching 3 from the left side.

A: we have to find limit value as x approaches to 3 from left side.

Q: Determine |7x + 42|| lim x + 6 x - -6 + |7x + 42 | lim x + 6 X- -6 -

A:

Q: Determine lim,-∞ *) . x+1 x+7x (주 00 1 -00. - T-

A:

Q: Prove lim-13x+2=-1

A:

Q: 1 4 lim 2--2+ x – 2 In(2x – 3) -

A: We have to find out

Q: Evaluate lim 2x - x-3

A:

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

A:

Q: Find the limit. 28x-7x lim x4 x→4 2-x 2. 28x- 7x lim 日 x→4 2- Vx (Type an integer or a simplified…

A: The solution are next step..

Q: Compute lim tan x→3+ -1 х2-9

A:

Q: 3 Find limx-2 Using a table. х-2

A:

Q: Explain the meaning of lim f1x2 = - 0. xSa"

A: Given:                   limx ς a+ f1x2=-∞   To determine:                        Meaning of this…

Q: 13) Determine the lim X--9 + 169 く+9

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 4- Prove that lim- tan 2x 5-lim 2(-3+x)²-18) x-0 X-0 2.

A:

Q: Evaluate x2 lim За - 10 - x→-2 x + 2

A:

Q: 2. Evaluate lim (5x - 2 x+3.

A: To evaluate the limit: limx→∞5x-2x+3 Solution: We know that, limx→afx-gx=limx→afx-limx→agx Using the…

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

A: By the €-δ definition of limit,

Q: -3x3 Evaluate lim Зд3 — 42 + х — – 10 - -

A: (1).    We have to find the limit: limx→∞ -3x33x3-4x2+x-10

Q: Construct a table to determine the lim ex-1/x.…

A: We will create a table to find the value of function close and close in the left and in the right of…

Q: Evaluate lim, --0( ) x \(4-x)2 16,

A: The given expression limx→01x14-x2-116

Q: 8. find limx>2 x-2

A: We have to find the value of limit

Q: ■ Find the limit.

A: We have to find the limit: limx→-3+x+2x+3 Since x→a+ denotes the right hand limit of the function.…

Q: Prove lim x ---> 3    (1/3x+1) =2

A: It is known that if we have a function f(x), and limit x tends to a, then the function can be…

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.