Discuss the continuity of : Q1 x+ for *く0 for osr<1 S(x)={ for Isx<2 -1 for X= 2 for r> 2 Q2 1-x lim

Q: Evaluate the limit.

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Q: 3 find the limit if it exists .If it do esn't exist, explain why. lim 13+x| X-> -3 2(34+X)

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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)…

Q: 2. Use the ɛ-d definition of the limit of a function to prove that lim = 3. I-»3 T – 2

A: Let  I  be an open interval containing  c , and let  f  be a function defined on  I , except…

Q: Evaluate lim z²-4z+3 z-3 O 1 O 3 O limit does not exist

A: Given function is, limx→3x3-4x+3x-3

Q: Find the constant a such that Va ax +4-2 lim

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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: Solve for the limit: lim \belowx → 3 x2-9 O a. 1. 54 c. 6. 1 54 O d. 1/9

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Q: Evaluate: lim ||r||; where ||r|| is the greatest integer less than r. I3- 3. 2.99999 Limit Does Not…

A: Given:      limx→3-x    Move the limit inside  the absolute value signs.      =limx→3-x    Again…

Q: 1. Determine whether or not each of the following limits exists as a real number or as +oo or -oo.…

A: According to the given information it is needed to check whether the limit of the following…

Q: Evaluate the limit: lim z-10 sin (4z)

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Q: Let n be a positive integer. For which n are the two infinite one- sided limits lim 1/x" equal?

A: Let n be a positive integer. for which n are the two infinite one sided limits limx→0±1xn equal. for…

Q: Use definiction to १r० v of Conkegene to lim n+4

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Q: 5. Use the Squeeze Theorem to evaluate lim sinz 1-00

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Which of the following statement(s) is TRUE? 1. lim,0 = 1. x2 V1-x? II. lim,→1 does not exist. 2а —1…

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Q: Show that |x2-4|&lt;e ,  when 0&lt;|x-2|&lt;e(5+e)-1 and prove limx-&gt;2 x2=4 by using these…

A: Note: The statement is verified by the ϵ-δ statement of limit.

Q: (2) Show that Jo for a > 0 but not for a = 0. lim 818 √ne-na² da a lim √ne-na2 748 da

A: We have to show that,   limn→∞∫α∞ne-nx2dx = ∫α∞limn→∞ne-nx2dx  for α&gt;0  but not for α=0.

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: 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: 4-IS. 2-x s (x)< 2Cos(x) for all x then find: lim f(x)

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Q: 4x In z (a) Evaluate lim エ→1( (1- 2)-- -1) C.

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

Q: 4-IS. 2-x s Mx) s 2Cos(x) for all x then find: lim f(x)

A: It is an application of sandwich principle of limit

Q: 2. Let r > 1. Prove that lim r" = 00,

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Q: Let a and b be positive real numbers. Evaluate lim (ax – Vax – bx) in terms of a and b.

A: To evaluate limx→∞ax-a2x2-bx where a and b are positive real number

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: 3. Show that if x > 0 for all n e N, then lim(x,) = 0 if and only if lim(1/x,) = +oo.

A: Consider the given information. xn&gt;0 and limxn=0 Now, use the limit definition of the sequence.…

Q: (7) ifa lim has a point that the equalio- prove PCz,y) is above L and only if 3x +2y >4

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Q: Find the limit: lim cos(5log6(7^x)) x-&gt; negative infinity

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Q: (A) Find the following Limits. x + 5 2. limy-3 f (x) if f(x) = }2x²+4 , x 4

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Q: 2. Use Squeeze Theorem to find lim,x f(z), if for all z >4 6e - 15 < {(x) < VI- 2 2e

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Q: 22- 7x + 12 Use continuity to evaluate lim In Use that In r is continuous on (0, x - 4

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Q: 8. Evaluate the limit. VI +5+ (In x)10 3/T+10+ (In x)20 (a) lim

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Q: Find the limit. 1. lim (1.001)* 2. lim (1.001)* ズー ex -e -3x 3. lim 4. lime 3x -3x e* +e*

A: Topic = Limits As per guidelines , At a time only three sub-parts can be answered. Please repost for…

Q: Show that lim (1 – 2²)"dr 0, n 00 0,

A: To show limn→∞∫01(1-x2)ndx=0 without attempting direct intergral.

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: 7. Compute the limit to infinity: 4-2+3r+1 a lim 7+3r-r+ 12

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Q: 3. Determine the following limit. () 2-x2 – 1 lim 3. x--00

A: We need to evaluate the value of the following limit limx→-∞3e22-x2-1

Q: Prove that lim r = 2 using the e-8-definition. Hint: VI - 2 = VT + 2

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Q: If lim(x,) =5100, then (Xn) is bounded. Select one: O True O False

A: 1) Here, lim (xn)=5100 that is finite. That is the sequence xn is bounded. So, the statement is…

Q: 4. Find the following limits or determine that they do not exist: 1+1/x a. lim,-0 1+1/x² 1+1/x? b.…

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Q: Q1. Compute the following limits if it exists. √x+2-3. 1-lim( x-7 2-lim (7x²+x+1) x→∞0 4x²+3x

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Q: II. Evaluate each of the following limits. 1-V3-x 4) lim x→2 4-x2 5) lim x→∞ 3 Sin ) 2 6) lim(4x +…

A: We have to evaluate the given limit.

Q: 2. Construct a table of values to investigate the following limits. 2r +1 lim a. 42 I-3 I+3 if z1

A: This is a problem related to the limit and continuity. Limit of the function is exist if right hand…

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

A: Zero

Q: Use continuity to evaluate the limit. 12 + Vx lim x-4 V12 + x

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Q: Recall that lim sup an = inf sup{am : m n}. n Assume that an 2 0. Show that lim an = 0 if and only…

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Q: Evaluate the limit, if it exists.

A: We have to find limit: limx→-414+1x4+x Since it is 00 indeterminate form so making it determinate by…

Q: 4. Use continuity to evahuate the limit. 5+ V lim X4 V5+x b) lim e-x X-1

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.