Find the limit: lim, 0+ x(ln x)²

Q: Find the limit (if it exists). If it does not exist, explain why.

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Q: 2/ Find the value of the limit: lim x/*,

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Q: Find the limit. 500 lim x→+00 ex i

A: From the given problem: limx→+∞x500ex So, we can also write as: y=limx→+∞x500ex Now take log on both…

Q: Find the limit, if it exists.

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Q: Find the limit using L'Hospital's Rule. lim x→0+ \x еx — 1/

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Q: Find the limit, if it exists, or type N if it does not exist. lim(x,y)→(0,0)  4x^2/3x^2+2y^2

A: Find Limit

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

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Q: Compute the limit or state that it does not exist. (If an answer does not exist, enter DNE.) xy2 lim…

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Q: Find the limit : lim,-0 tan(пx)

A: We have to find the limit of given function when x approach 0.

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

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Q: Find the limit. (If an answer does not exist, enter DNE.) lim x+0 x2 + 6x

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Q: Find the limit. (If an answer does not exist, enter DNE x + 1 – 2 lim x→3 X - 3

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Q: Evaluate the limit: lim (x - ln x)* x→0+

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Q: Find the limits

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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’Hôpital’s Rule if necessary.

A: L'Hopital's rule states that,  for two functions f(x) and g(x) such that, limx→cf(x)=limx→cg(x)=0 or…

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (x, y) → (0, 0) x0 + y…

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Q: Express the limit by Epsilon delta definition (a) lim,-9 x² – 9x = 25

A: We will answer the first question as per our guideline. Please resubmit the other questions…

Q: Find the limit. lim tanh(x)

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Q: Evaluate the limit: sinx lim x→0 e4x – 1

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

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Q: Find the limit, 1 lim xž sin(-) 3

A: Given: limx→∞x32 sin1x   L'Hopitals rule: limx→cf(x)g(x)=00 or ±∞∞ then…

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

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Q: Find the pointwise limit lim_(n→∞)(ex/n/n) for x ∈ R.

A: We find the pointwise limit  lim_(n→∞)(ex/n/n) for x ∈ R.

Q: Find the limit. sin2x lim x→0sin7x

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Q: Find the limit lim (r+ e").

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Q: Calculate the limit algebraically. lim (x + Jx)

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Q: Use l’Hospital’s rule where applicable to find the limit.

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

Q: Find the limit. If the limit does not exist, explain why. Vx-/2y lim (x,y)→(4,2) x-2y

A: Factories the denominator term and cancel out the common from numerator.

Q: Find the limit, if it exists. lim X 00 4X + sin x 2.

A: Our aim is to find the limit of the following:limx→∞  24x+sinx  = ?

Q: Find the limit. X400 lim x→+o er %3D i

A: find limx→+∞x400ex=?

Q: Find the limit. lim sin(x8)

A: We have to find the limit.

Q: Find the limit of the function along the x-axis xy lim (x.y)-(0,0) x2 + y?

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Q: Approximate the given limit numerically and verify your answer graphically. VI+4- 2 lim

A: we have the limit  limx→0x+4-2x

Q: Find the limit analytically. If the limit does not exist, write DNE. lim X0 Lx 4+x

A: limx→0 1x14+x-14

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x²yeY (x, y) → (0, 0) x4…

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Q: Find the limit. lim etan x→(3t/2)+ х

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Q: Find the limit. 3x3 lim (x,y) →(1,-2)1+x2 00 0-12120 O 1 ula 0-1/105 O

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.)  lim Δx→0+…

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Q: Find the limit. lim sech(x)

A: Given:limx→∞ sechx

Q: Find the limit: lim, +0+ (sin¯' æ)"

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

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Q: Find the limit, if it exists.

A: Find the limit, if it exists.

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

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Q: Find the limit. lim sin-2x i

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Q: х, x 1

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Q: Find the limit by interpreting the expression as an appropriate derivative. e2x lim- 1 i X0

A: As we already know that, dydxx=a=limh→0f(a+h)-f(a)h

Q: Find the limit. (e-sx cos(^) lim X- 00

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Q: Find the limit. (e-2x cos(x) lim

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Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.