Given that2x - 2< g(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: 21 f(x)= 3x2 +4x +1 and g(x) = x2 -2x-3, then what is lim f(x) *→19(x)?

A:

Q: find the limit or explain why it does not exist. x2 – 4x + 4 lim x3 + 5x² 14x a. as x→ () b. as x→2

A:

Q: Use algebra to evaluate the following limits. x-6 a) lim x6 3x² - 12x - 36 x² + 2x² + 7x 4x b) lim…

A:

Q: State whether the inequality provides sufficient information to determine lim x➔ l f (x ), and if…

A:

Q: lim (x3 +x

A:

Q: Given lim f(x) = 7 and lim g(x) 8, evaluate: %3D x8 x8 lim (7f(x) + 5g(x)) = %3D lim (7+ 5f(x)) = 7…

A:

Q: Evaluate the limit. Vx2 lim x² + 3 3x2 + 1 x- 00

A:

Q: Evaluate the limit: x² +6x+8 ]im as x – – > - 4 lim x-4 x+2x-8 2 x ^ 2+ 6x + 8 divided by x ^ 2+ 2x…

A:

Q: Given that2x – 6 <g(x) <x² – 2x-3, use the Sandwich Theorem to determine lim g(x). X→3

A:

Q: What is lim f(x)? X-1

A: Given graph: To Find: limx→1f(x)

Q: Solve the problem. Given that f(x) = 5x², find lim [f(x) - f(4)/(x - 4)]. X-4

A:

Q: The value of the limit 2-x3 lim x2+3x3 is Select one: -1/3

A: The given expression is limx→∞2-x3x2+3x3

Q: a. Using the Sandwich Theorem to find: lim f (x) If v5 – 2x2 <f(x)< V5-

A:

Q: r+ 2 Calculate the limit lim 1-2 x2 – 3x – 10°

A: By using L'hopital's rule, we find the limit of the function.

Q: Compute

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

Q: Evaluate in terms of the constant a.

A: We have to find the limit in terms of constant a: limx→02a+x This is determinate limit so we need to…

Q: If lim x->3 f(x)=7 which must be true? f is continous at x=3 or f(3)=7.

A: I have given you detailed solution with detailed explanations... So  you will face no difficulty to…

Q: Evaluate the limit: 6x 12 lim I> 2 r2 + 3x 10

A:

Q: Evaluate in terms of the constant a. lim (2a + x) x→ 0

A: To Determine:  Evaluate in terms of the constant a.…

Q: Given: x + 1, -2 < x < 0 x = 0 0 < x < 2 x = 2 2, f(x) = -x, 0, 2 < x < 4 х — 4, What is the lim…

A: Consider the given function. fx=x+1,          -2&lt;x&lt;02,                x=0-x,…

Q: Find a number b such that lim- .2. x²-4 =2 x-b x-x -2

A:

Q: find the limit or show that it does not exist for lim x→−∞ √4x2 + 1 / 2x + 5 .

A: limx→-∞ 4x2+12x+5 = limx→-∞ x4+1x2x2+5x                                =limx→-∞ 4+1x22+5x…

Q: If 2x < g(x) < x* – x² + 2 for all x, find lim g(x). x-1

A:

Q: Use the definition to show that x2 + x -6 lim = 5. x - 2 4.

A: I have just used the definition of limit

Q: what is the lim x->0  f(x)-f(0)/x^2 if f(x)=2x^2+1?

A:

Q: Given: f (x) = -3x2 - 1 Find: lim, 1 (f (x))

A:

Q: If f(x) = 3x2 - 4x +1 and g(x) = x² + 2x - 3, then what is lim 9X, g(x). X-1 f(x)

A:

Q: If 3x – 2 s f(x) < x² - 3x + 7 for x 2 0, find lim f(x). X3

A: 3x-2≤f(x)≤x2-3x+7

Q: Given f(x) = 3/(4-x)3 , evaluate limx=4+ f(x)

A:

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: (b) Given that lim f(x)== 2 and lim g(x) =4 , find the limit x→2 x→2 1 lim 3f(x)- Vg(x) x→2 Using…

A:

Q: x-2 51. lim x-1x-1

A:

Q: Find limx∞ h(x), if it exists, f(x) = 5x3 − 3…

A: Given: fx=5x3-3

Q: 4x + 12 lim 2 x 3 x²9

A:

Q: If -a2 + 6x – 7 < f(x) < 2x – 3 for all r, find lim f(x). Cite any relevant theorems used.

A: Given that,  -x2+6x-7≤fx≤2x-3 To determine limx→2fx. By the algebra of limits, If gx≤hx  then…

Q: Evaluate in terms of the constant a.

A: Given :            limx→ax-ax-a

Q: Evaluate the limit lim x² + + 6x + 18 – x - x 00

A: Given

Q: If 8x – 19 < f(x) < x² + 4x – 15 determine lim f(x) x→2 What theorem did you use to arrive at your…

A:

Q: If  2x ≤  g(x)  ≤  x4 -x2 +2 for all , evaluate  lim x-&gt;1g(x).

A: Given  2x ≤  gx  ≤  x4 −x2 +2 for all To find: limx→1gx

Q: If p(x)=x²+2x -3 and q(x)=x3-1, then lim 3p(x) 4q(x) x+1 II

A:

Q: Use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.   limx→8f(x)=

A: To use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.

Q: 2. Complete the table and use it to find lim numerically. x-2 x -2x-8 -2 x² +2x x² - 2x-8 x² +2x lim…

A: Explanation and solution is given below....

Q: Use the –δ definition to prove that lim x→1 (3x + 5)/2 = 4.

A:

Q: Find the value of lim f(x), if f(x) = x3+ 6x + 2 x 3

A:

Q: (b) Given that lim f(x) == 2 and lim g(x)=4 , find the limit x2 1 lim 3f(x)- Vg(x) x→2 Using the…

A: Given thatlimx→2f(x) = 2  and limx→2 g(x) =4    and we have to find the value of the limit…

Q: If 3x-35f(x) < x²-3X+6 for X z0, find. lim f(x)

A:

Q: Given that f(x)={kx2+2,≤22kx,x>2. If limx→2f(x) exist, then k equals.

A:

Q: Given that2x - 2< g(x) <x2 + 2x 3, use the Sandwich Theorem to determine lim g(x).

A: