9 -x2 if x < 1 Let g(x) = %3D cx + 4 if x > 1 .What value of c makes g(x) continuous at x = 1? Show all conclusions. 2 Vx-4 Using the appropriate precise definition of limit, prove that lim,44

Q: 2n3 +1 1 Prove, using definition of limit, that lim 4n3 – n 2 n-00 -

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Q: 3 Find the limit: lim t 3 et – 1 - (Enter undefined if the limit does not exist.)

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Q: See pencil for correction of problem

A: First we simplify the expression (x2-2x-8)/(x+2)=(x2-4x+2x-8)/(x+2)…

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Q: Let f(x)={−2x+2  x≠1               {2   x=1. What is f(1)? If f(1) does not exist, type: 99999 What…

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Q: 2) By using E-S definition of limit, show lim (x+y+xy)cos÷ cos 음-0 COS (xy)(0,0)

A: Let f(x)=x+y+xy cos1x cos1y

Q: 9. Evaluate the limit. lim (1+ sin 3x)1/x x→0+

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Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x,y)→(0,0) x²+y2

A: To show that the limit of a multivariable function does not exist,…

Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

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Q: Let Sz+8 3x +8 I-1 Approximate lim f(z) numerically and verify your answer graphically. If it does…

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Q: 4. Does f(x) = : (0, 00) → R have a right limit at x = 0? If yes, compute the limit. If not, explain…

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Q: 10. Let a be a positive constant. Evaluate lim x(a/x – 1) if the limit exists. If the limit does not…

A: limx→af(x) does not exist. The idea is that there is no number that f(x) gets arbitrarily close to…

Q: Let f(x)={−2x+2   x≠1               {−5         x=1. What is f(1)? If f(1) does not exist, type:…

A: Given,

Q: V-1- x + 2 if x -- 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A:

Q: Q4 Evaluate the limit lim (x.y)-(0,0) 3x2+y xy cos y if it exist. If not, show that the limit does…

A: In this problem we compute the limit along x axis and along the line y=x .If these two limits are…

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Q: limf(x) does not care what happens While a limit exactly at x = c because the limit is concerned…

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Q: 8 - x- x2 if x 4 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

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Q: 1 if x – 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x -…

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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: If x4 &lt;=ƒ(x)&lt;= x2 for x in [-1, 1] and x2&lt;=ƒ(x) &lt;= x4 for x &lt;-1 and x&gt; 1, at what…

A: Summarizing the given information:             . We need to find out that at what points c, we…

Q: 5x2 + 10x + 1 20. lim x* + x² + 1

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Q: 5) a) If a > 0, compute lim a¯*. b) Which approaches its limit faster as x→», y=2* or y=x²?

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Q: 2+4x 7. Prove lim = 2 using the e-ô definition of the limit. 3 %3D X-1

A: Hey, since there are multiple questions posted, we will answer first question of the first image. If…

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

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Q: The limit lim (n+1-vn- (A) equals-x (B) equals 1 (C) equals ( (D) equals +∞ O(E) does not exist

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Q: (4- x - x² if x ≤ 2 2x-7 if x > 2 Calculate the following limits. Enter "DNE" if the limit does not…

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Q: 8- x- x2 if x 3 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x)…

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Q: V-1- x + 5 if x - 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand side limit of the…

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim-(7/2)-(tan x)cosx (2) limy-0…

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Q: 1 Let f(x) According to the definition, 7 4x f'(x) = lim h0 (Enter the limit in reduced form) %3D

A: Givenf(x)=14x-7

Q: 3x²+2x- 3 3. prove that with the help of the limit definition (with necessary analy si)

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Q: Q4: - Evaluate the limit of the following: x3–1 sin 2x 1-V 1) lim 2) lim x→0 2x²+x 3) lim x→1 1-x…

A: When we get 00form, we can us  L' Hospitals Rule to calculate the limits. In this rule μx→a…

Q: 2 – x x2 if x 5 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

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Q: - x – x2 if x 2 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

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Q: 9 if - 1 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = 2 -1…

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Q: 2. Find the limit of the following function sin(x - 4) lim- x-0 x- 2

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Q: 4 Using the e- 8 definition of limit, prove that lim I-3 3r 1 2 -

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 5. Evaluate the limits using any of the methods you know. Show your work. In(1+4x) c. lim tan 2x

A: find the limit

Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x.y)-(0,0) x²+y2

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Q: 4. Use the e - 6 definition of limit to show that lim (2: +3i) = 2 + 5i. 2+1+1

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Q: [ 2 Let f(x) x – x2 if x 3 - Calculate the following limits. Enter "DNE" if the limit does not…

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: 2. Determine the infinite (∞ or -0) limit as follows: x² – 2 - (a) lim x2- x2 3x + 2 - 4-6 sin x – 1…

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Q: 4 Using the e – 8 definition of limit, prove that lim x→3 3x 1 1 2

A: To prove the limit of given function using the epsilon delta definition of limit which states that…

Q: 4] [2M] Determine whether the limit exist in R for lim xsin(1/x²), (x# 0). x→0

A: Zero

Q: 6 -- if a - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

A:

Q: Suppose lim g(x) = 4, lim f(x) = 0, lim h(x) = -5. %3D Xa Xa Find following limits if they exist.…

A: It is given that,  limx→ag(x)=4,  limx→af(x)=0,  limx→ah(x)=-5 we have to solve, 4) limx→ag(x)f(x)5)…

Q: Q1:Find the limit using L Hopital rule In (csc x) lim xT/2 (x – (1/2))²

A: Given limx→π2ln(cscx)(x-π/2)2 We have to find limit by using L Hospital rule L'Hospital's Rule…

Q: 6 - x - x² if x ≤ 1 if x > 1 2x - 9 Calculate the following limits. Enter "DNE" if the limit does…

A: f(x)=  6-x-x2    if x≤1 2x-9         if  x&gt;1