We are building an oblique tower from n pieces of iden- tical, homogeneous blocks on a horizontal surface, ac- cording to the figure. What is the maximal possible dis- tance d by which the top- most block is shifted hor- d (n) izontally relative to the block at the bottom? Describe the positions of the blocks in this extreme case and determine the function d(n). What is the limit of d(n) as n → ? (The blocks have unit length.)

Q: (a) By using the definition of limit, prove that lim (3x+i z31

A: Introduction: Limits in mathematics are distinct real numbers. Consider a real-valued function "f"…

Q: Use l'Hôpital's Rule to evaluate the limit. .3 8x +7 2, lim X- 1 X1 O A. 11 O B. 19 C. O C. - 16 D.…

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Q: 1. Use the e - ô definition of the limit to show the following: (a) lim(5x – 2) = 3 (b) lim VT = 0

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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: Determine if the pointwise limit lim_(n→∞)(ex/n/n) for x ∈ R is uniform. If yes, is the limit…

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Q: Let f(x) = /3r – 10. According to the definition, f'(r) = lim h0 (Enter the limit in reduced form)

A: f(x)=3x-10f'(x)=limh→0f(x+h)-f(x)h

Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

A: Given that, limx→02xexlnx+12 According to L-hospital rule limx→0fxgx=limx→0f'xg'x, if fxgx is 00 or…

Q: Evaluate the limit with either L'Hôpital's rule or previously learned methods. 5t In(t) lim t- o 8 +…

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Q: Evaluate the limit V9n1 + 13n' = 5n – 10 lim =V25n16 +5n2 -9n Also, find the asymptotic value of…

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Q: and If lim f(x) = lim g(x) = +o and flx) =1 and gtxl = e, what is the limit of the division of !!…

A: As given limit is infinitely by infinity form so use L'hopital's rule and substitute the given…

Q: Evaluate the limit using a definite integral 2 lim n n 1+

A: Let x = i/n Hence, dx = 1/n when i = 1; x = 1/n; As n tends to infinity, 1/n tends to zero. Hence,…

Q: 17. Use the limit process to fnd the anea of the negion bounded by the graph of f(x)=2x43 ón the…

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Q: Evaluate the limit using L’Hôpital’s Rule.

A: Given limit: limx→-4 2x2+13x+20x+4

Q: Evaluate the limit using L’Hôpital’s Rule

A: We use the L’Hôpital’s Rule to find the limit

Q: Let f(x) = 2x² + 2x + 3. According to the definition, f'(x) = lim h→0 (Enter the limit in reduced…

A: the soluton is following.

Q: Evaluate the one sided limits of K at x=L algebraically using ly Usina a plecewise formula for…

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Q: If the limit does not exist, say why. (If the limit does exist, so state.) -The limit does not exist…

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Q: Evaluate the limit using L’Hôpital’s Rule

A: The given limit is limx→∞5x2-3x+13x2-5.

Q: Evaluate the limit using L’Hôpital’s Rule

A: Given limit is: limx→∞x3+2x4-x We have to evaluate it by the method of L'Hospital's rule, So…

Q: 3. Prove lim(a – 5x + 6) O using the epsilon-delta definition of a limit.

A: Explanation of the answer is as follows

Q: 4) Make a table for a sequence of carefully chosen values of a to estimate the limit 1® – 1 f(x) =…

A: By using table value of x for this given function to estimate this given limit

Q: t2-3t+5 lim -1+ 0 t

A: Given:        limt→0et−1t+t2−3t+5t2−1

Q: Use the definition of the limit ( epsolon - delta ) to show that lim of 1/z as z approaches -i

A:

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: Evaluate the limit using the Basic Limit Laws

A:

Q: Evaluate the limit using the Basic Limit Laws

A: Given: Let y=limt→43t-14t+1 To Find: To evaluate the given limit.

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

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Q: 2. Find the following limits. Show your work. Vx2 + x – 1 lim (a)

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Q: t2 - 1 lim t→-2 t2 +3t-1

A: Given limit is limt→-2t2-1t2+3t-1.

Q: lim -y3-3y²+4 y--2 -2y2-y+6

A:

Q: 9) Find the limit. lim f (z) æ – 2| ( (z) = 2- 2 Graph method

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Use the two-path test to prove that the following limit does not exist. y-2x2 lim y+x (x.y)-(0,0)

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Q: Using the elpison delta defination of a limit prove that the limit of (5x+7)=2 as x approaches -1…

A: Given function is  f(x) = 5x +7

Q: Evaluate the limit using L'Hospital's rule.    limit of 4cos(3x)sec(-7x)  as x approaches pi/2

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Q: Given that g(x) = 2ª + 2 is continuous on its entire domain, find the limit of the g(x) as x…

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Q: By using the L'Hopital's Rule, find the limit of the following functions. (b) 14х — 12| lim X→3- х —…

A: Answer

Q: Use the Squeeze Theorem to find the following limit when b - |x - al s f(x) sb + x - al. lim f (2)

A: 1.b-x-a≤f(x)≤b+x-alimx→af(x) Note:     Multiple questions are given, we are answer with only one…

Q: Evaluate the limit V9n4 + 13n³ – 5n – 10 lim -V25n16 + 5n² – 9n Also, find the asymptotic value of…

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Q: Find the maximum value of 8 > 0 that satisfies the limit claim corresponding to ɛ = 0.1, that is,…

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Q: Calculate the limit algebraically. (If an answer does not exist, enter DNE.) x2 + 3 lim x--2 x2 + 3x…

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Q: 3. Compute the limit algebraically Vx +3x2 lim 6x 1

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Q: What result do you obtain when you evaluate the limit (RHL and LHL) of the limit of (x^2-16)/(x-4)…

A: Given f(x)=x2-16x-4 LHL=limx→4-f(x) and RHL=limx→4+f(x) Here if LHL = RHL, then limit exists.

Q: et –1 t2 – 3t + 5 lim t-0 t t2 – 1

A:

Q: Use the definition of "limit of f at c" to prove the limit of lim, 3(x² – 5x + 1) = -5

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Q: 3. Compute the limit algebraically Vx + 3x2 lim 6x 1

A: Solution: The objective is to find the limit of the given function

Q: Compute the limit of the function at −1 AND determine if the function is continous at 1. f (x) = {…

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Q: Evaluate the limit using l'Hôpital's Rule. x3-64 lim X-4 X-4 а. 48 O b. 12 O c. 16 O d. 0

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Q: ) Evaluate -The limit (lnx) as approaches positive infinity (a 1 Zero e O Infinily

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.