51. Given ɛ > 0, find an interval I = (5, 5 + 8), 8 > 0, such that if x lies in I, then Vx – 5 < ɛ. What limit is being verified and what is its value?

Q: Evaluate the following by limit of su (3x² +5)åx (sin x)dx

A: Solution:To find the integration Formula:∫xndx=xn+1n+1+Csin2x=1-cos 2x2∫cos ax=sin axa+C

Q: Find the limit  x appraoaches infinity (e - 2x cos x)

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Q: Show that the limit does not exist: limit    (x^2+y-2)/(x-2y+4)                    (?,?)→(0,2) I…

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Q: Estimate the limit numerically. ++7,000x³+ 800,000 lim 2x° + 1,269x³ 8. O to∞ 2.

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Q: Determine the following limits analytically.

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Q: Show that the following limit fails to exist by showing that the limit is different for two…

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Q: Compute the indicated limits. 2x + 5 lim cos 3x? + 2x – 5

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Q: Evaluate the following limit using L'Hospital's rule: 1 - x + ln x lim x→1 1+ cos(3rx) CoS

A: Value of limit is  0 Explanation is given below

Q: Compute the following limits if they exist: sin 2x – 2x (a) limit sin 2x - 2x +у x3 + y (b) limit…

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Q: The limit as x approaches infinty of (x+3^x)/(x^2-3^x) Evaulate using L'Hospital's Rule providing a…

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Q: 2. Use L'Hospital's rule to evaluate the following limit. cosh(3x) – 1 lim x→0 x2

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Q: I need help evaluating this limit. Please refer to the attached picture.

A: Before evaluating the limit, let's simplify the given function. Please see the white board.

Q: 7 Find lim cos - Enter I for o, -I for –∞, and DNE if the limit does not exist. Answer:

A: Given query is to find the limit of the expression.

Q: Express the limit as a definite in 7 lim 1 + (i/n)3 n→ 0 n i = 1 1 7n dx 8

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Q: Express the limit as a definite integral. 4 lim non + (i/n)- (i/n)9

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Q: (a) Determine the following limits without using L'Hôpital's rule. V7x° +4x -x² -2 lim x'-2x-3x+1…

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Q: Express the limit as a definite integral. n 7 lim 8 1 + i = 1 n- o n dx

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Q: If x > 8 and x n+1 - - for nEN. Then the limit of x is equal to 11 X 21

A: Given that, If x1&gt;8 and xn+1=2-1xn for n∈ℕ. The objective is to find the limit of xn.

Q: 6 Use the e - d definition of a limit to prove e lim 1+2 r2 + 2 1.

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Q: Compute limit as x goes to infinity of (cos(x))/(x)

A: We find: limx→∞cosxx We solve this limit by using Squeeze theorem. Squeeze theorem states that if…

Q: Use l'Hôpital's Rule to evaluate the limit. 2 - 4x+2 lim 2. X>co X+5x+11

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: 27. a. Show that the area A, of an n-sided regular polygon in of radius r is a circle sin nr2 2т A,…

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Q: Compute the limit as x goes to 0 of [tan(x) - sin(3x)] / (x^2)

A: limx→0[tan(x)-sin(3x)]x2=[tan(0)-sin(3(0))]02=00

Q: a In x (b) lim 100 I+ In x

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Q: what is the limit as n goes to infinity of enn! divided by nn?

A: Since e^n &gt; n And rate of convergence (e^n × n!) &gt; rate of convergence (n^n)

Q: 2. Compute xe" da using a limit.

A: The given which we have to find the integration from 0 to ♾️  f(x) = xex

Q: 4. Evaluate the limit of as e approaches 0. 2a A 2 B. % CO D. infinity

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Q: y om U to 1.0 how can you find limits bntegroutlon.

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Q: Use l'Hospital's Rule to calculate the exact value of the limit ) as x→ 0- Az) fX) = e -1 and g(x) =…

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Q: Evaluate the given limit. Show your complete solution. limo(-x ln(sin(4x² + x)))

A: The given limit is limx→0-xlnsin4x2+x. We have to solve the limit using L'Hpotial's rule.

Q: sin(72) lim 2-16 In(z – 5)

A: find limz→6sin(πz)ln(z-5)

Q: = 2 -- for n E N. Then the limit of x is equal to n+1 If x,> 8 and x ******

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Q: To prove that the limit of f(x)=x^2+4x as x approaches 2 is 12, given any ε>0, c that 6-min{4,k).…

A: Epsilon-Delta Definition of Limit : A limit limx→af(x)=L is defined as : If ∀ ε&gt;0 there exists a…

Q: Use two different methods to find the limit where m &gt; 0, n &gt; 0, and x &gt; 0

A: The given limit is: limx→∞lnxmlnxn where, m &gt; 0, n &gt; 0, and x &gt; 0 First method: To evaluate…

Q: What is the limit as t goes to 0 of    4 tan^-1(t)

A: Topic:- limit

Q: 00 *tan(1/r)=? O a. 2 O b. 00 O c. Limit does not exists

A: You know:

Q: 5. Use the concept of limits to solve for the following problem iz3 – 1 lim z-1 z + i

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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: 8. Express the limit as a definite integral and evaluate. 4i 7cos 3- lim i=1

A: Limits as a definite integral and evaluate

Q: 1. Prove the following limits x 4y4 G) lim (x,y) (0,0) (x²+y4)3 = Does not exist

A: Solution is given below:

Q: Use l'Hôpital's rule to find the following limit. 1 1 1. x-2 In (x-1) X-2+ 1. x-2 In (x-1) 1. |(Type…

A: Given query is to find the limit of the expression.

Q: 1-e * xp- By using the limit comparison test, the integral 1. x2 + 1

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Q: Express the limit as a definite integral on the given interval. lim x, In(2 + x^)Ax, [3, 4] n- 00

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Q: Let f(x) 2.x – 5 if x > 5 --- Calculate the following limits. Enter "DNE" if the limit does not…

A: Here we have, f(x)=10-x-x2 if x≤52x-5         if x&gt;5 We have to calculate,…

Q: 1-e X x2 +1 X By using the limit comparison test, the integral

A: Using, limit comparison test

Q: Express the limit as a definite integral. n lim 2 20 AxK, where P is a partition of [ - 6, 1] ||P|→0…

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Q: 1. Use the limit definition to evaluate ,(2 – 3x)dx.

A: The given integral is ∫-122-3xdx

Q: Evaluate the following limit: tan(4x“ + 4y*) 4x2 – 4y? lim (z,y)→(0,0) 8x4 + 8y4 x – y O 2 1 2 The…

A: Functions of two variables continuous. Using two path test.

Q: Compute the following limit.“ KC'arctan(2t³ – 1) dt] du (x – 1) In r lim Be sure to explicitly…

A: We have to evaluate a limit and we will use the L'hospital's Rule to find the answer.