5. State whether the inequality provides sufficient information to determine lim f(x), and if so, find the limit. x→1 (a) 4x – 5 < f(x)

Q: Find the limits lim х2 — 1 as a. x→1+ b. x→1 c. x→-1+ d. x→-1

A: we have to find the limit    the given expression is

Q: 3. Explain why the following limits do not exist. 1 (a) lim x-5 (x-5)2 -x² +3, (b) lim h(x), where…

A: (a) limx→51(x-5)2 Let  f(x)=1(x-5)2 As x approaches 5, (x-5)2 approaches 0, and so f(x) approaches…

Q: 2/ Find the value of the limit: lim x/*,

A:

Q: 2. Use the definition of the appropriate limit to show (a) lim→∞(2x² + 4x – 1)/(3x³+ 1) = 0. (b)…

A: a) Given limx→∞2x2+4x-13x3+1

Q: 1) Find the Limit lim/→0 3x²h-7th+h h

A:

Q: Find the limits lim (V² + 3 + x) X -00

A:

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: lim (4.x – 3) = 9

A: The given limit,      limx→34x-3=9

Q: Estimate the limit numerically. x² lim +14x+49 -7 x+7 O-7 Oto∞ O-1 00

A: Given limit is We will use the factorization method to evaluate the limit By using the result that…

Q: Find the limit L.

A: We have to find the limit L: limx→4x+2 This is determinate form of the limit so we need to put limit…

Q: 1.) Calculate the limit: lim(2x² – 6x +1)

A: We have to find the limit of the function: limx→22x2-6x+1 Since this is determinate limit so we just…

Q: lim 2x x→0+

A: We are given the limit : limx→0+eπx-2x1x Formula to be used here : If limx→af(x)=1 and…

Q: Find the limit L.

A: Given, limx→2x2-3 To find the limit of above expression.

Q: Give the two-step method for evaluating a limit of the form lim f(x)8(x).

A:

Q: Find the limits x² - 7x lim X-o X + 1

A: Given: limx→∞x2-7xx+1

Q: Find the limit, if it exists. 1) lim (x2 + 8x - 2) X→1

A: =?

Q: 3. Evaluate the limit of lim(x² + x + Vx + 1) x→3

A: A limit of a function f(x) is defined as a value, where the function reaches as the limit reaches…

Q: Find the limit.   Lim  x→1+      x1/1-x

A: Given function is By property of logarithm

Q: Evaluate the limit. lim x² In x x→0+

A:

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

A: limx→0--4+x2x2

Q: lim(4x – 3) = 9 x→3

A:

Q: 5. Evaluate the limit: Vx +1 lim x→1 4x -4

A: Limit at a point exists if left-handed and right-handed limits exist and they are equal. Left-handed…

Q: Verify that L’Hôpital’s Rule applies and evaluate the limit.

A: Consider a function fx. The limit of a function at x=a is given by: limx→a fx=fa

Q: Find the limit. lim x2/(1-x) X→1 *

A:

Q: a) Find the limits: 1- lim- X-1x-x 2- lím 0 V+4-2 5x 3- lim

A:

Q: 1- Evaluate the following limits, if they exist. If they do not exist, state why. a- Lim 4 c- lim…

A: See the details solution in below

Q: Calculate the limit algebraically: x³ + 8 lim x→-2 x² + 7x + 10

A: Consider the given expression, If we substitute  in the expression we get  form. so, use L-hospital…

Q: Q2: Find the limit x + 3 lim x→-3 x2 + 4x + 3

A: We have to find limit

Q: ■ Find the limit.

A: Given: limx→∞ x2 - x4   To find: Value of the limit.

Q: V x2 + 9 - 5 lim X→-4 x + 4

A:

Q: Evaluate the limit algebraically. 1 х — 4 - lim x→4 x + 4 x2 – 16 If the limit does not exist enter…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Evaluate the limit, if it exists.

A: We have to evaluate the limit: limx→164-x16x-x2 It is 00 form, since there is square root function…

Q: 3. Find the limit of +2x+3 lim X-2 V x+5

A: As per Bartleby guidelines, we will solve only first question To find the limit of limx→2x2+2x+3x2+5

Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: Use the theorems to evaluate the limit. 1 lim x → ∞ x2 ||

A: We have to evaluate the limit.

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: Q2: Find the limit r + 3 lim x-3 x + 4x + 3

A: We have to find limit

Q: Use the theorems to evaluate the limit. 1 lim x →∞ X² ||

A:

Q: Use the formal definition of a limit to show lim (2x + 1) = 5. x+2

A: Given: limx→2 2x+1=5

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: 1. Use the definition of the limit to prove the following limit. 1. lim x = 3 x→3 2. lim x +x–11=9…

A:

Q: lim(4x – 3) = 5 x→2

A:

Q: Calculate the limit algebraically. lim (x +2) O -2

A: Given limit is  Since the function f(x)=x+2 is defined for x=2, therefore, we will evaluate the…

Q: 5. Use a table of values to estimate the value of the limit. a). f(x) = lim x² -3x est –1 b). f(t) =…

A: Gg

Q: Find the limit. /x² +3 - 2 lim X- 1 X1

A:

Q: 5, evaluate the limit. 2x3-x 5) lim X0 x2+3x-1

A:

Q: (b) Find the following limit: 4x +5 lim x+2 2x -1 (i) (ii) lim 4 x+* x* -x' +2

A: The solution is given as

Q: 6. Explain why the limits lim f(x+h) – f(x) and lim f(2) – f(x) h Z-X are each initially in the form…

A: Given that the limits are limh→0fx+h-fxh and limz→xfz-fxz-x.

Q: Evaluate the limit. x2 + 2x – 15 lim- x – 3 X-3

A: