1. Find a) lim x+3 3-x b) lim x3* 3 - x c) lim- +3 3-x d) the vertical asymptote of f(x)= 3-x

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

A: Given limx→0e3x-3x-14x2

Q: 2) lim () – X-00

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Q: 1- Find the limits: lim V - 1 メ→ x-1 а. 2x3 b. lim x- 00 3(x-2)2 2x3 c. lim x2 3(x-2)2 x+1 d. lim…

A: Consider the limits  a.limx→1x−1x−1b.limx→∞2x33x−22c.limx→22x33x−22d.limx→3x+13−x2

Q: 3. If lim f(x) = 5 and lim f(x) = 5, what can you say about x1 X1+ lim f(x)? What can you say about…

A: Definition used -       Limit of a function -       The limit of a function at point x=a…

Q: 1. Find the value of lim (5x – x*), or state that it does not exist. Either way, explain in words.…

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Q: Find the limits a) lim x2 - 4x + 3 x2 - 1 when x approaches 1 b) lim 6x + 100 7x2 100 when x…

A: We have to find the limit

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

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Q: 2 3 Determine the limit: lim x1- 2- 4x + 3

A: To determine left hand limit of given function.

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

A:

Q: (b) With the help of Sandwich theorem (or Squeeze theorem), show that lim (2 √√x - 1)" = x² for x ≥…

A: By using Sandwich theorem,  we have to show that ;   limn→∞2xn-1n = x2  for x≥1

Q: Let f(x) = 3x + 2. Use the € – d definition to prove that lim 3x +2 1. x→1 Definition. E-d proof.

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Q: 5. What is the sign of the coefficient multiplying x' if f is a polynomial of degree 7 such that lim…

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

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Q: 1- Find the limits: VI- lim X X-1 а. 2x3 b. lim x→ 00 3(x-2)2 2x3 с. lim x2 3(x-2)² x+1 d. lim X-3…

A: Given: )

Q: 1- Find the limits: lim x→I x- 1 а. 2x3 b. lim x- 00 3(x-2)2 2x3 c. lim x-2 3(x-2)2 x+1 d. lim x-3…

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Q: 7. For the limit lim (x³ - 3x + 4) = 6 illustrate Definition 2 by finding values of 8 that…

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

A: limx→0--4+x2x2

Q: Use limits to determine the equations for all horizontal asymptote.  y = (1 - x2)/( x2 + 1)

A: To find the horizontal asymptote using limit we find the limit of y when x approaches infinity.…

Q: What are the limits of both parts of this question?

A: In part a, there is no bound, so the answer of the limit is infinity.

Q: 16. Evaluate using L'Hospital's Rule. x3-216 a. lim X-6 (In x) b. lim 4x2

A: Given, Part a: limx→6x3-216x-6 If we put x=6 we get an indeterminate form, Therefore by using the…

Q: Use limits to determine the equations for all horizontal asymptotes. 1- x y = x² + 1

A: To determine: The horizontal asymptote of the given function with the help of limits. Given…

Q: Determine the infinite limit. x2 – 3x lim x-3+ x2 - 6x + 9 00

A: Taking the common terms from numerator and denominator for simplifying the expression

Q: 4-VE Find the limit: lim→16 x-16

A: We need to evaluate the following limit limx→164-xx-16

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

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

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Q: Given a function f:R → R with f(x) = x - 1, for x rational and f(x) = 5 - x, for x irrational Prove…

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Q: 2- Determine lim[ v( x-1000)+10]/x x-0

A: Given problem:-

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: Find the value of a such that exists and find the limit. limx-> -1 (2x2-ax-14)/(x2 -2x-3)

A: Given, limx→-1(2x2-ax-14)(x2 -2x-3)

Q: 1. Evaluate the limit: 5 - x lim x→5+ (x – 5)2

A: Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: Determine the infinite limit. x² - 4.x lim 1+4+ x2 - 8r + 16

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Q: 1. Using L'Hospital's rule, evaluate lim(1 – x²).

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

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Q: 2 Find the limit or show that it does not exist. 8. lim (/4x2 + 3x + 2x) X→-0

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Q: 1. Find the limit. x² - 25 lim x 5 x² - 8x + 15 ૨૨

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Q: (3) Find the limit. 1- x lim 1+3- X – 3

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Q: 1- Find the limits: Vx- 1 lim xI x-1 а. 2x3 b. lim X- o 3(x-2)2 2x3 c. lim X-2 3(x-2)2 x+1 d. lim…

A: Given: a)  limx→1x−1x−1=?b)  limx→∞2x33(x−2)2=?c)  limx→22x33(x−2)2=?d)  limx→3x+1(3−x)2=?

Q: 1.) Determine the limit: a) lim vx2 + 14x + 49 x-5 b) lim (x² – 4x)³ x-1

A: Solution:To solve 1a and b1.(a)limx→5x2+14x+49(b)limx→1x2-4x3

Q: 1 1 Find the limit lim *+5 8 x→3 x-3

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Q: Determine the infinite limit. x2 + 6x lim x-3 x2 – 6x + 9 8

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Q: B. If k is any real number, prove or disprove that sinkx 1. lim x-0 kx = 1.

A: We will prove this by L'Hopital's rule

Q: Let x2 + 10x + 21 f(x) = x2 + 12x + 35 The expression using limits to calculate the equation of the…

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Q: 2. Evaluate the limit: 1000 lim TC lim -7)2 (8-x)3 x→8+ x+7-

A: The left-side of the limit of a function at a point is the value of the function when the value of…

Q: Find the limit. x* – 1 - lim x→0+ In (x) +x – 1 п lim ( 1+ n

A: These question is based on Limits.

Q: 1. Find a) lim b) lim x→3* 3-x c) lim=-, d) the vertical asymptote of f(x)=- x→33-x 3-x

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Q: Evaluate the limit lim x² + 4x – Vx² + x ) and interprete the result in relation to x 00…

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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

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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

Q: Find all values c such that lim x-2 2c²x 5c +1 x²-3x + 2 - exists. (a real number)

A: We say a limit exists if right hand limit and left hand limits are same. We have…