True or False: If lim f(x) = 3 and lim g(x) = 3. then lim[–3f(x)² – 49(x)] = False True

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

A: Given limx→0e3x-3x-14x2

Q: then

A: The given statement is False.   The detailed solution is as follows below:

Q: 3x -4x b) lim X→-00 x2-2x3

A:

Q: (2x-1)(3-x) is (x-1)(x+3) limx→0

A: Given problem is :

Q: x² +2x - 3 Evaluate lim -5x?

A:

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

A:

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

A:

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

A: Solution:Givenlimx→∞ x-34x2+25To find the limit valueFormula:ab=ab

Q: Hence, find the value of lim f(x). x→-3 lim f(x) Enter your next step h x→-3

A: Given,          Consider the graph of a function, fx , shown below :

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

A:

Q: х3-x2-5х-3 (х+1)* (iii) lim x-1

A:

Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: x2 + x -6 2. Use the precise definition of a limit to prove lim2 x - 2

A:

Q: If lim f(x) = 15 and lim g(x) = 25 then x5 x5 lim 3f(x)g(x) –- 6] = x5

A: Given that limx→5 fx =15  and limx→5 gx=25 find limx→5 3fxgx-6=?

Q: Find the limit. lim x→3 1−x2/(x-3)2

A: Given, The limit limx→3 1-x2x-32  We have to find the limit.

Q: (b) Prove that lim,→20,¤€A ƒ (x) exists and is equal to lim→0 Yk-

A: This problem is related to the sequence of functions. Given:  fkk∈ℕ is a sequence of functions from…

Q: Find Limit Using Squeeze Theorem: 2. If 2x – 2s f(x)<x² – 4x + 3 for x 2 0, find lim f(x).

A:

Q: (a) lim n-0 2 – ni x² – 4 (b) lim x + 4 x² – 4 (c) lim x – 2

A:

Q: Let F(x) = (x2 + 3x + 2)/(2 - | x | ). Make tables of values of F at values of x that approach c =…

A: Given: Fx=x2+3x+22-x To determine: We have to estimate limx→-2Fx by making a table of values of F at…

Q: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

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

A:

Q: Prove that lim x 2 = 4. x→ 2

A:

Q: (a) lim x→2 arctan(7-3x)-" 2х-4 4 (b) 10-e5x lim x→00 16-x2

A: See the calculation and explanation below

Q: 5) Does the limit |x+1| lim x-1 x+1 exist? If yes, find its value, if not - explain why. Show all…

A:

Q: If 2x+2 ≤ f(x) ≤ x2 +2x+2, for all x, then find lim f(x) x-> 0

A: Given

Q: x³ - 3x² + 2x Evaluate lim - using l’Hôpital's Rule and then х — 2 check your work by evaluating the…

A: Given, limx→2 x3-3x2+2xx-2

Q: V2x –1 Using defination of limits, prove that lim Vx- 3 L^ = X4

A:

Q: 5. If lim f(x) = 8 but lim f(x) does not exist, what can you X+2+ X+2 say about lim f(x)? X2-

A: We know that, limx→afx=l, if: limx→a+fx=limx→a-fx=l

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

A:

Q: 2) Find lim f(x). X→1 f(x> X 2. 2.

A: here      limx→1- f(x)=1    and            limx→1+ f(x)=2 here                            limx→1-…

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

A:

Q: d the limit lim X-3 x-2-1 x-3

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Q: Find the constant c so that the limit limx->3 (x2+x+c)/(x2-5x+6) exists.

A:

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: Given f(x) = 2x^2 + x -15 all divided by x+3 find lim x -> -3^f(x) algebraically is f(x) continous…

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Q: find lim x-> infinity (V 4.x +x + 2x) or show it does not exist. cannot use l'Hospital's rule. must…

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Q: How do you solve question 5 and 6?

A:

Q: Evaluate lim (e* – 2.x) x→0-

A: To evaluate: limx→0-(e3x-2x)3x

Q: x² - 5x – 24 lim Calculate the limit: x-3 x+3

A: the given limit is: limx→-3x2-5x-24x+3 we have to evaluate the given limit.

Q: c) lim -4e-x

A: c) limx→∞-4e-xlimx→∞-4ex

Q: 3. Show algebraically that lim x* – 2 – x = 0

A:

Q: x2 X tet tx et + 1 A. lim x 2 B. lim - 3-1 2 - C. lim x⇒1 x² + x 2 x² - 1 Remember that if you…

A:

Q: Find the limit.

A: Given,

Q: 3. Prove lim 3x-7= 2 X-3

A:

Q: Investigate the one-sided limits graphically: (a) lim x→2# x – 2 (b) lim x→0± x2 (c) lim In x x→0+

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Q: the limit is negative infinity enter "-INF". x2+4x-12 lim→2 x2 –4 x2 +4x–12 lim→-2 x² –4 x2 +4x–12…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Evaluate A) lim x͢ 1 2 x2 + 5x + 7. B) limx͢.-4 (√x2 + 9 – 5)/(x+4

A: Consider the given limit: A) limx→12x2+5x+7B) limx→-4x2+9-5x+4 Here, the objective is to find the…

Q: Find lim I -4 2+1 1 lim z - -4 +1 Show your work and explain, in your own words, how you arrived at…

A:

Q: Given that lim f(x) = 4 and lim g(x) = -2. Find the value of x-2 x-2 lim 4f(x) + x-2 [g(x)]³ ) 2

A: we find the value of given limit