7.)For the function g whose graph is shown, find a number a that satisfies the given description. (a) lim g(x) does not exist but g(a) is defined. (b) lim g(x) exists but g(a) is not defined. エー>a (c) lim_g(x) and lim g(x) both exist but lim g(x) does メ→a+ not exist. (d) lim g(x) = g(a) but lim g(x) # g(a). %3D x a

Q: 7ーズ 1. Find lim using a. Table of values f(x) b. Limit rules

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

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Q: Formally prove that lim 2x+3=7 using the ɛ,8 definition of a limit. x→2

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Q: Determine the limit by sketching an appropriate graph. V16-x2 Osx< 4 lim f(x), where f(x) = 4 4sx<8…

A: GRAPH

Q: Calculate the limit limx→13√x−1x−1.

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Q: DRAW THE GRAPH OF A FUNCTION WHERE limr-a f(x) DOES NOT EXIST FOR SOME INTEGER a. EXPLAIN WHY THE…

A: To draw a graph of function where limx→afx does not exist for some integer a

Q: Find the limit, if it exists.

A: Consider the given: limx→∞ x21−8x2Divide numerator and denomintor by "x2",limx→∞ x21−8x2=limx→∞…

Q: 2. Explain why f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths…

A: A number L is said to be the limit of a function f(x,y) as (x,y)→a,b , if for any real number ∈&gt;0…

Q: 2. Write the equation of a function that is discontinuous at x=5, but lim f(x) exists, and is…

A:

Q: x-2 a) limy-2+ x2–4 - 4

A: We have to find limit

Q: Draw a graph where lim x→2 f(x) exists but f(x) is discontinuous at x = 2. Name the type of…

A:

Q: Calculate the limit lim 2√(x-4) / (x-4) As x goes to 4

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Q: 3. Use the precise definition of a limit to prove lim(9 – x) = 5

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Q: Determine the limit: 12x - 10| lim %3D 5 - x X5

A: To find  The given limit

Q: 3. Determine the infinite limit. x² + 3x lim x--1- x2 + 2x + 1

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Q: lim M18

A: See step 2

Q: lim(4x – 3) = 9 x→3

A:

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

A:

Q: Show that

A: Here we have to show that;  limx→-∞1x

Q: Estimate the value of the limit lim, 4 x² + 1 by filling out this table and then making an educated…

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Q: What must be multiplied to both numerator and denomination of lim→2 3-г-1 SO 2-x that the limit will…

A: We have to find multiplication factor for given Limit.

Q: 10. Use the definition of limit to show that a. lim (x² + 4x) = 12, Z-2

A:

Q: suppose f(X)->  -250 and g(x)->0 with g(x)>0 as x->2. Determine lim->2  f(x)/g(x)

A: Given: limx→2f(x)=-250 and limx→2g(x)=0 and g(x)&gt;0

Q: Calculate the limit if it exists: lim x→4 for 5/(x-4)2

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Q: 4. Find the limit: lim (b) lim -5x+4 x-4 X-4

A: We can find the limit using the L'Hospital rule.

Q: Establish the x² - x + 1 lim +2 3 %3D By using the 4. x+2 € - 8 definition of limit or the…

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Q: Find the one-sided limit (if it exists).

A: Given :                       f(x) = limx→2- 1x2-43

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: If lim f(x) =5 x-->1- and lim f(x)=5 x-->1+, what can you say about lim f(x) x-->1? What can you say…

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Q: Estimate the limit numerically for lim X4 x²-3x-4 4 3.9 3.99 3.999 4.001 4.01 4.1 X. x - 4 Lx2 - 3x…

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Q: If f and g are two functions such that lim f(x) as x --> a = + infinity and lim g(x) as x --> a = +…

A: Given: f &amp; g are two functions such that, To check if this statement is True or False

Q: Evaluate the limit 6| lim x→6 x - 6. If the limit does not exist enter DNE. Limit =

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Q: estimate the limit numerically to two decimal places or state that the limit does not exist

A: The value of the limit is 2. Take the first term as common term and simplify.

Q: Show that lim- e +1 does not exist. 1/x

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Q: Find the limit x-5 lim x→5 x²-25

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Q: Evaluate the limit  Limx-&gt;0 (ex-1-x)/x3

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Q: Find the limit or show that it doesn't exist. 1-х-х2 a) limx→-o 2х2-7 V1+4x6 b) limx 2-х3

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Q: lim(4x – 3) = 5 x→2

A:

Q: 5) Find the indicated limit if it exist. 3- Vx + 7 а) lim x→2 2 - x x' +1 b) lim х>-1 х+1

A: (a).    We have to find the limit: limx→2 3-x+72-x

Q: Compute the indicated limit. „2 x + 3 lim x00 x - 4

A:

Q: 3- If lim f(x) = 3.5 and lim,2+ f(x) = 6.5 , the function has a double sided x-2- limit or one sided…

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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: 3 lim - 1 x² + x – 2) X-1

A: By L'Hospital 's Rule limx→1 (xx-1 - 3x2+x-2) =limx→1(x(x2+x-2)-3(x-1)(x-1)(x2+x-2))…

Q: Find the limit or show that the limit does not exist. lim→-0 4x2 + 3x + 2x x→-∞

A: See the details solution in below

Q: 1) If lim f(x) = , what asymptotic behavior will be illustrated in the graph of f (x)?

A: 1) If limx→6-fx=∞, then the value of the function fx tends to infinity as x→6 from the left hand…

Q: Evaluate the limit, if it exists. lim (1/4+1/x)/(4+x) x--&gt; -4

A: The given expression is,

Q: 2) If 2 – x2 < f (x) < 2+ 3x² whenever -1 < x < 1, use limit theorems to find lim0 f (x). Give all…

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Q: 6 Find the value of a such that 2x2 - ах — 14 lim х-1 х2 — 2х — 3 exists, What is the value of the…

A: The limit of a function at a point 'a' in its domain is the value that the function approaches as…

Q: Find the limit or show that it does not exist lim 212 + 3t – 5

A:

Q: Prove lim(3x–10) =-4 using the ɛ, d definition of a limit. 2

A: Recall: ε -δ Definition :Let f be a function defined in a deleted neighbourhood of 'a' . Then a real…