Prove that both (a) lim inf y, 2 lim inf r, (b) lim sup y, < lim sup r„.

Q: Prove the limit statements lim x sin = 0 y=x sin 2

A: Prove the limit statements     limx→0x sin1x=0

Q: Prove that lim [f(r, y) + g(x, y)] = L, + L2 (K, y) (a, b) where f(x, y) approaches L, and g(x, y)…

A: Given : lim(x, y) → (a, b) f(x, y) = L1     ...(1)lim(x, y) → (a, b) g(x, y) = L2    ...(2)   To…

Q: Formally prove that lim 2x+3=7 using the ɛ,8 definition of a limit. x→2

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Q: (b) Show that if lim sn = +o∞ and lim tm > -x, then lim($n + tn) = +0.

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Q: Prove that lim r(x)= where m = 0, 1, 2, 3. .. II

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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: Prove rigorously that lim lxl = 0.x→ 0

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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: 1. Prove lim, n+2n³+7 2 0, using the definition.

A: I have used only definition of limit of sequence

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: Prove that lim |x|sin(1/x) = 0.

A: We need to prove that limit of given function is zero.

Q: Prove that lim (2a2 + 3r + 6) = 5 using the e, 8 definition of a limit. %3D a -1

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Q: 8. Using squeeze theorem, show that the following limit (x – 1)² In x = 0. lim (x,9)→(1,0) (x – 1)²…

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Q: Find Limit Using Squeeze Theorem: 2. If 2x – 2s f(x)<x² – 4x + 3 for x 2 0, find lim f(x).

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

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Q: Prove that lim(x,y)→(1,2) (x2 + 2y) = 5 by using the precise definition

A: ε-δ definition: Limit of function f(x,y) at a point (a,b) is 'L' if for every ε&gt;0 there exist…

Q: lim -1 x→0+

A: Separate the limit.

Q: Prove that lim r(x) = 0 where m = 0, 1, 2, 3. ...

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Q: Prove limx→∞(1/x)=0

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Q: Prove that lim (r2- 1) = 3 using the e, 8 definition of the limit. %3D 141 Linh tL

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Q: . Use the definition of limit to prove lim = 2r - 3 = 7.. %3D %3D

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Q: Find the required limit or indicate that it does not exist. lim o+ (in (t6), 12 in t O 6i O Does not…

A: We have to find out

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: Use the e – 8 definition of the limit to prove that lim x2 – 2 = 2. %3D - x→2

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

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Q: Use the Squeeze Theorem to show that lim (x2 sin(2)) = 0 x-0 %3D

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Q: swer of the following lim 2x²+6y² lim (x,y)→(0,0) x²+y²

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Q: 8. )Prove that lim Vr = 2 using the e-8-definition. Hint: VI – 2 = x- 4 VI + 2 Puouo thot thoro…

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Q: Prove that lim,→3 3x – 7 = 2 by using e, d definition of limit.

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Q: Using the ɛ, & definition, prove that lim V = 1. %3D x 1

A: We have to prove the given limit.

Q: 1. Prove that lim vx sin O using the Squeeze Theorem.

A: Using squeeze theorem,

Q: Prove the statement using the ɛ, d definition of a limit. 1. lim (x² – 4x +5) = 1 x→2 2. lim (x² –…

A: use the definition of epsilon and delta definition  to prove the limit.

Q: Use an appropriate definition to prove the following limits. x³ – 16x* = 1 I+0 r°+ 4x² x +2 V9x2 + 4…

A: This is a problem of limit . Based on the formula and concept we will answer the question.

Q: Prove, using the formal definition, that lim→-1 (T+1)² +0o. %3D

A: We have to find the limit limx→-13x+12=+∞.

Q: Compute the following limits if they exist. 2 - VE (a) lim 244 3 - V2x + 1 (b) lim r sin

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Q: Calculate the limit limx→0cos3x−cosxx2.

A: To Determine: calculate the limit  Given: we have limx→0cos3x-cosx2 Explanation: we have a function…

Q: Prove that lim (2x – 7) = 3 by using the e, 8 definition of a limit. x→5

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Q: 2х — 5 lim 4x

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Q: Suppose there is a number B such that |f(x)/x| < B for all x # 0. Then prove that lim f(x) = 0. 1.…

A: Given that: |f(x)/x|≤B

Q: Prove rigorously that lim sin 1/x does not exist.                                    x → 0

A: Let the given limit be y - y = limx→0 sin1xy = limx→0 sin1x1x×1xy = limx→0 sin1x1x×limx→0 1xy =…

Q: Show that the lim Z→0 |Z| does not exist.

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Q: 2. Use e -d of the limit to prove that lim z= 4

A: Given below the detailed solution

Q: 2) Show that the limit exists : 3x3 ,3) lim (x.y.z)-(0,0,0) x2 +y² + z2

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Q: use the squeeze/sandwich theorem to show that lim x--&gt;0 (x^4cos(1/x)) = 0

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Q: Find Limit Using Squeeze Theorem: 3. If 2x s g(x) s x* – x² + 2 for all x, find lim g(x).

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.