Use limit theorems as needed to evaluate each of the following limits; if a limit is a real numbe it; if a limit is infinite, find which one (i.e. ∞ or -0); and if a limit does not exist, then write DN (x+ 1)(x² – 4) lim x* — Зх + 2 x-2 Зx? — 5х — 2 lim X-2- |x' – 8|| 3

Q: 4 lim X-0 x2 2 1-cosx

A: Given- limx→04x2-21-cosx To Find- The value of the limit.

Q: use l’Hôpital’s Rule to evaluate the limit

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Q: 1 (i) lim 3n2 – 4000 のlim(- 2n2 +10000 X00

A: Topic:- calculus

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) x + 1 lim X→3 X - 3

A:

Q: Use l'Hôpital's rule to find the following limit. 3x-2x lim 3 X o 5x° +3

A: To use the L-Hospital rule to find  Lim(x tends to infinity) [3x³-2x]/[5x³+3]

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→∞  √(x+3x^2)/2x-1

A:

Q: Consider the following. lim (4 – x) X→3 y 3 2 1 2 4 Use the graph to find the limit (if it exists).…

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Q: Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) 2√x lim CSC X

A: Explained below

Q: Evaluate the limit using L'Hospital's rule: e10x – 1– 10x - - lim x2

A:

Q: 1. Use the e-8 definition of the limit to show that x3 – 2x + 4 lim X-ix2 + 4x – 3 3 !3! Use the…

A:

Q: Find the limit L. Then using the Epsilon Delta definition to prove that the limit is L  lim x→−4…

A: Given,

Q: Q4 Evaluate the limit lim (x.y)-(0,0) 3x2+y xy cos y if it exist. If not, show that the limit does…

A: In this problem we compute the limit along x axis and along the line y=x .If these two limits are…

Q: Find the indicated one-sided limits, if they exist. (If an answer does not exist, enter DNE.) S-x+7…

A:

Q: Is there a real number a such that 3r + ar + a+3 lim --2 r+x + 2 exists? If so, find the value of a…

A:

Q: Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) lim 8x sec ax…

A:

Q: Evaluate the limit, using L'Hôpital's Rule If necessary. (If you need to use co or -, enter INFINITY…

A:

Q: analytically

A: As per the guidelines we can solve 3 parts only.

Q: Find the indicated one-sided limit, if it exists. (If an answer does not exist, enter DNE.) lim X-0-

A:

Q: Find the indicated one-sided limit, if it exists. (If an answer does not exist, enter DNE.) Vx + 5…

A:

Q: Find the limit by L'Hospital's rule (whenever app 1 cos(x)-1+x a) lim- 2x4 b) lim

A: Explanation of the answer is as follows

Q: Evaluate the following limits using the limit theorems. Show your solutions. 1. lim (4x – 7) X-0 2.…

A:

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x to 0 (9x^2 - 6x / x)

A: We first factor the numerator

Q: Find a value of the constant k such that the indicated limit exists. 8 -5 lim x-0 ekx +5

A:

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) 2. lim

A: For a one-sided limit, check for any vertical asymptote (if exists).

Q: Find the following limit. lim (5x)6x X+0+ lim (5x)ôx | (Type an exact answer.) l X-0+

A: Given:

Q: Find the limit. (If the limit is infinite, enter 'o' or '-∞', as appropriate. If the limit does not…

A: Answer(a): The given limit is: limx→∞e-x+3cos7x Now, apply the limit property…

Q: Find the limit. 6x + 2 lim e 6x+ 2 =(Type an exact answer in terms of e.)

A:

Q: Evaluate the limit, using L'Hôpital's Rule if necessary. (If you need to use co or -co, enter…

A:

Q: Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) lim x+x* csc x

A:

Q: Find the limit. (If the limit is infinite, enter '' or '-', as appropriate. If the limit does not…

A: Find the limit

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→0  x −…

A: We have to estimate the limit numerically if it exists.  a) limx→0(x-3) b) limx→0(x-1)

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) x – 1 lim x- -0 x2 + 5

A:

Q: A function is said to have a horizontal asymptote if either the limit at infinity exists or the…

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Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A:

Q: Q1:- Find the limit for each of the following functions if is exist ? 1) lim|x – 3| x-3 sx + 2 ,…

A: We find limit of given function

Q: Find the limit, If it exists. (if an answer does not exist, enter DNE.) lim

A:

Q: Evaluate each limit WITHOUT using a table of values. If a limit does not exist, write DNE and…

A:

Q: Find the one-sided limit L (if it exists). (If an answer does not exist, enter DNE.) Ilm ++ (x-2) x-…

A: As, Given, limx→0+x-1x3 The function decreases without a bound. So, limx→0+x-1x3 = - ∞

Q: Use the precise definition of a limit to prove the following limits. Specify a relationship between…

A: To Prove - limx→3 x2-7x+12x-3 = -1Cosidering LHS - limx→3 x2-7x+12x-3 = limx→3 x2-3xx-4x+12x-3limx→3…

Q: find the limit, if it exsits, or show the limit does not exist. lim (a2 * (1,y)-(0,0) sin²y)/(x² +…

A: Given:f(x)=x2 sin2(y)x2+2y2To find:We have to find the limit of the function

Q: Use the precise definition of a limit to prove the following limits. Specify a relationship between…

A: Given limx→3-2x+8

Q: 1. Find the following limits if they exist, whether they are a real number or too. If a limit does…

A:

Q: Use the precise definition of a limit to prove the following limit. Specify a relationship between e…

A:

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 4x + 4 lim x--1 x + 1|

A: To find limx→ -14x+4x+1

Q: ........ ........ Find the limit. (If the limit is infinite, enter 'o' or '-o', as appropriate. If…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→0  x6 cos(5/x)

A:

Q: Suppose lim g(x) = 4, lim f(x) = 0, lim h(x) = -5. %3D Xa Xa Find following limits if they exist.…

A: It is given that,  limx→ag(x)=4,  limx→af(x)=0,  limx→ah(x)=-5 we have to solve, 4) limx→ag(x)f(x)5)…

Q: Verify that L'Hôpital's rule is of no help in finding the limit; then find the limit, if it exists,…

A:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) (x2 – 4x + 6, 1-x² + 4x –…

A: Here we find limx→7fx       where fx=-x2+4x-2, x≥7x2-4x+6  x <7if it exist

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.