If ,Vn € N, then lim 2"x, equal to and In+1 1+ (a) (b) (c) (d)

Q: Prove that lim +1) = 3 using the e--definition.

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Q: 1-z = ? What is lim %3D !- 2!- -2

A: In order to evaluate the limit of a function f(x) at certain point a then replace x by a to get…

Q: by L'Hopital's rule 3sin e -1 lim

A: limθ→03sinθ-1θApply L-Hospital Rule

Q: What is lim x=inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^(3n)] + 2? (express answer as x,y)

A: Solve the following

Q: 3. Evaluate lim, tan (2 x) if it exists. Provide evidence to back up your answer.

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Q: Prove the lim(Sn) = -∞ case.

A: We use the notation uN =inf{ sn :n>N},              vN =sup{ sN : n>N }, u = lim uN = lim inf…

Q: prove limx->a 1/x = 1/a with epsilon-delta definition

A: We need to prove the given problem using the epsilon-delta definition.

Q: by L'Hopital's rule 3sin e _1 lim

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Q: Prove that lim, = 1, (x > 0).

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Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2? (express answer as x,y)

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Q: Prove that lim, Vn = 1.

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Q: 5. lim X-0 e2x-1

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Q: Show that limx,y)-(-2,0) g(x, y) does not exist given that (x + 2)³y² (x + 2)6 + 3y4' 0, if (x, y) +…

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Q: Show limx→∞ xne−x = 0 for all n = 0, 1, 2, . . . . To get started notice that when x ≥ 0, all the…

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Q: Compute, from first principles, without using L'Hopital's rule eh – 1 lim = 1 h-0 h

A: (18) We have to evaluate the limh→0eh−1h. We know that the expansion of eh, which is given by…

Q: lim 21/* is no limit 1

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Q: 1 1 Use l'Hopital's rule to evaluate lim x→0+ In(1+x),

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Q: 5. If lim f(x, y) = 5 (x,y)→(3,–7)" %3D for every curve C in R? containing the point (3, -7), what…

A: If limx,y→3,−7fx,y=5  is true, then it represents that limit exists atpoint (3,-7) for function…

Q: Find the lim inf (xn) and lim sup (xn) of Xn=3-(-1)"

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Q: 1 1 lim xV1+x

A: limx→01x1+x-1x=limx→01-1+xx1+x

Q: Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a…

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Q: Find (if exists). lim (х,у) — (0,0) (4 + (x² + y²) In(x² + y²; Dose not exist O 4 0 1 0

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Q: & Prove that lim I = 2 using the e-d-definition. Hint: Vr %3D

A: Given: To explain the given statement as follows, Here, prove that limx→4 x = 2.

Q: 5. Prove that lim Show your t→-2 t+2 complete solution.

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Q: Prove that lim x->0+ √ x [1 + sin2 (2 π/x)] =0

A: Given: limx→0+x1+sin2 2πx By using the property of limit, the limit of a product is the product of a…

Q: Show that lim sin( does x→0 x2 .not exist

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Q: If(z)- 니 < e. By definition Show that: lim, »1+i = - а. b. 4 lim = 2i. %3D 2- 1-i z2

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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: lim (1+e9)°

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Q: Q. Prove that: Lim tanhx =1 .

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Q: (i) Evaluate In (1-z³) lim 2->0 sin (2z

A: We need to evaluate the limit If the value of the function after putting the limit is in the…

Q: Let m and n be two positive integers greater than 1. ecos (α"). am m then the value of (1) is n If…

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Q: Hws] lim x = 5 E 5e •Prove

A: Given sequence xj=5j-1j+2j∈N we have to find limj→∞xj limj→∞5j-1j+2=limj→∞j5-1jj1+2j       (Taking j…

Q: lim cas z is nonexistent

A:

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: Find lim (e-2x cos x) (Hint: Squeeze Theor

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Q: ах Determine the values of a and b such that lim Vax +b – 3 = 5. x→0 bx

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Q: 2. Use L'Hopitals's rule to find lim (-).

A: Given that: limx→0+1x-1ex-1

Q: 5. Prove that if lim g(r) = 0 then lim g(x) sin () = 0. %3D

A:

Q: 44

A: To prove,

Q: 2) G VALUATE THE UMIT, IF IT EXISTS. Lim X-3 x2-X-12 uT x²+ 3x 2)

A: Given:         limx→-3x2+3xx2-x-12   Factoring                   =limx→-3xx+3x-4x+3

Q: lim x in (It -)

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Q: We have lim I- a Vsing 1-x = (- Fa)(+Ta) So, lim 1- Fa lim - a 거- (1-「 (i+Tx) %3D lim ス→) as 1+ T…

A: Yes your solution is correct

Q: Evaluate lim S", r³dx . O 4 Does not exist.

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Q: Prove using the def. Of a limit (b) limx→0(2x^2) − 3)) = −3

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Q: lim sec(4+x?)' Ax where Ax = 12-(-3) and x; = -3+iAx.

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Q: 2. If (xn) and (Yn) are sequences of real numbers such that lim (xn) + 0 and lim (xn Yn) exists,…

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Q: 1. Use the limit laws to evaluate lim (2x-1)Vx+3 In each step, indicate the limit law applied.

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.