Evaluate the limit using L'Hopital's Rule: 122 limg0 sin(3x)–3x O 12 48 9.

Q: if r = -1 Is f(r) = · continuous at r= - -1? (Show your work using limits.)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Compute this limit to infinity, no lhoptials rule   limx→∞ of x−sqrt(2x^2+ 1).

A: We have given limx→∞ of x−sqrt(2x^2+ 1).

Q: 10. lim (cos (1/x))'

A: The limit to be evaluated is limx→∞cos1/xx. The  L'Hôpital's rule: For limit limx→∞fxgx which is an…

Q: Use L’Hôpital’s Rule to evaluate the limit.

A: We have to evaluate the following limit: limit as x tends to zero, [sin (pi x)]/[sin (5 pi x)] using…

Q: 3. Use the epsilon - delta definition to prove that the limit is lim Vx x-0 371 when

A: To use epsilon delta definition to show that the below limit is 0. limx→0x3=0

Q: Show that the following limit ry lim (.v)-(0,0) 22 +y? does not exist.

A: Substitute y=mx, and check by applying limit.

Q: Find the limits in Exercise

A: Limits are used to calculate the approaching value of the function at which the exact value of the…

Q: Evaluate the limit using l'Hôpital's rule: - co X) lim 3x2

A: Differentiate two times with respect to x

Q: What go in the blank as limit approaches 0:

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Q: Evaluate the limit using L'Hospital's rule 8* – 3* lim X+0

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

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

Q: Find the limit: lim, G-). -i B) does not exist pdf.6 (A) يملع الانتقال إلى السؤال التالي إجراء تغي…

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Q: Use the definition of limit to prove lim (r+ 4y²) = 6. (2,y) (2,1)

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Q: Inx lim, V.r

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Q: Evaluate the limit using L'Hospital's rule ex – x – 1 lim X+0 9x2

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Q: Find the limit (if it exists). (If the limit does not exist, enter DNE.) - (x² - -/-) lim

A: The given limit limx→0-x2-3x

Q: Evaluate the limit lim sin-(÷).

A:

Q: Evaluate the limit using L'Hôpital's rule. limx→0  ex+2x−1/9x

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Q: limi

A: We have to use the definition of limit to determine L=limn→∞sin(n)n

Q: Use L'Hôpital's Rule to evaluate the limit L.

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Q: Evaluate the limit using l'Hôpital's Rule. (Inx) lim 7x

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Q: Use l’Hôpital’s Rule to find the limits

A: Given: limx→01x4-1x2 for finding limit , we simplify given expression by taking L.C.M.…

Q: Verify that L’Hôpital’s Rule applies and evaluate the limit.

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Q: lim r3/2 sin (1/x)

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Q: Vx? lim x-0 eVx-1-x

A: Given: The provided function is:…

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

A: Given: limx→0sin6x4x

Q: Evaluate the limit using L'Hopital's rule lim 4 cos( – 5æ)sec( – 3x) 2

A:

Q: use the epsilon-delta definition of a limit to prove that

A: We have the given limit limx→3x2+1=10. We have to use ε-δ definition to prove the given limit.

Q: Evaluate the following limit. (-) lim| costi- 5 sin j+-k 2

A: Given,            limt→πcosti-5sin-t2j+tπk

Q: 2r (1- lim

A:

Q: Evaluate the following limit using L'Hopital's Rule. Vx? lim x→0 eVx-1-x

A: We need to evaluate the limit  limx->0[ (28x2)/(e28x-1-x) ] by L'Hospital's rule

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: Evaluate the limit tan 5z lim I0 sin 2z

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Q: Use L’Hôpital’s Rule to evaluate the limit.

A: L'Hospital's Rule states that, The given limit is:

Q: 2r (1- lim

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Q: Evaluate the limit with either L'Hôpital's Rule or previously learned methods. 8e3x 8 lim x-0 sin(x)

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Q: Evaluate the limit using L'Hospital's rule et – 1 lim x0 sin(4x)

A: we have given limit, we have to find it's value using L' Hospital rule. lim x→0ex -1sin 4x

Q: Use L’Hôpital’s Rule to evaluate the limit.

A: This is in (0/0) form. Therefore we will apply L'Hospital's Rule to find the limit.

Q: Use the definition of the integral to write sec x dx as a limit. Do not evaluate the limit.

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Q: xy? lim (x,y)→(0,0) x² + 2y4 Compute the limit

A: Given limit,

Q: verify that L’Hôpital’s Rule applies and evaluate the limit.

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Q: Use the formal definition of the limit to prove the statement rigorously.

A: We know               -1≤sin 1x≤1 ⇒-x≤x sin 1x≤x

Q: Estimate the limit numerically or state that the limit doesn't exist: sec (2) lim (Enter DNE if the…

A: To estimate the limit of the given function at x->1+ . Since the given function is continuous in…

Q: Evaluate the limit using L'Hôpital's Rule. 3x lim x0 sin(x) - x→0 — х

A: From the given limit: limx→03x3sinx-x Now solve: limx→03x3sinx-x=303sin0-0=00    ....indeterminate…

Q: Find the limits

A: Given that limx→∞1x∫0xtan-1tdt . First integrate the interval in the given expression.…

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

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

Q: 8. Find the limit using squeeze theorm. lim x² sin(x²)

A:

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.