5. What appears to be the limit as Ax→0?

Q: х3 + 6x2 — 32 – 32 1. lim х--4 х3 + 5х2 + 4х

A:

Q: evaluate the limit using continuity. lim (х,у)-- (2, —1) (xy – 3x²y³)

A: Given: limx,y→2,-1  xy-3x2y3

Q: Write a limit using summations that would equal 0 tan (2x) dx.

A:

Q: How can the Approaching of  a Limit from One Side be done?

A: In calculus, a one-sided limit is either of the two limits of a function f(x) of a real variable x…

Q: 4 – 3" lim,40 -

A: Evalute this limit  problem lim(x tands to 0 ) (4x -3x )/(x). Here i attached solution of this…

Q: Describe in your own words what the Central Limit Theorem does for us.

A: The Central Limit Theorem :

Q: Note: Enter 'DNE' if the limit does not exist or is not defin

A: We have to evaluate the limit using the graph.

Q: What is a left-hand limit?

A: If the x values approach from the left side of a number, then it is called left hand limit.  For…

Q: In z O lim

A: Please refer the attached image for complete Solution.

Q: By(tty) tan (x*+9}

A:

Q: x2 + 8x – 9 4. lim x→1 x3 2а? — 5х + 6 - -

A:

Q: 1. Carefully explain how you know if a limit exists. What must be true about the left sided limit…

A: Given

Q: Show with the epsilon delta definition that the limit when x --> 4 of (x^3-8x^2+16x+4) = 4

A: we have to show with the epsilon delta definition that the limit when x→4 of x3-8x2+16x+4=4 as we…

Q: Compute limit as x goes to infinity of (square root(2x^2+3x-1))/(7x+1)

A: =limx→∞2x2+3x-17x+1multiply and divide by x2=limx→∞2+3x-1x27x+1x2=2+3∞-1∞7∞+1∞=∞

Q: Oevaluate the following limit by airect evalvatiun in C6x-る 3x -3

A: answer for given limit = 12

Q: Express the following limit as an integral. 7 lim Σ (5(at)* + 4x; - 6) Δr over 12,61

A:

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: given find the limit numerically limx→23x−95x−25

Q: Use L'Hospital's Rule to evaluate the limits

A:

Q: The central limit theorem refers to the fact that ?

A: We have to determine what Central Limit Theorem say about mean or sum of observations.

Q: How would this process look should we try to do it via limit definition (IE, (f(x+h)-(fx))/h)?

A: Derivative of g(x) at x=a=limh→0g(a+h)-g(a)h

Q: compute the limit (or state that it does not exist) assuming that lim n→∞ an = 2

A:

Q: O use the Limit definition of the deriviatune to find (verify using powter rule)

A:

Q: Evaluate the limit using L'Hospital's rule 1 lim 3xe 3x

A:

Q: 7 Write a limit using summations that would equal S Answer: lim N→∞ n k=1 [x³ - 4] dx. Submi

A:

Q: х4-81 (iii) lim х-з 2х2-5х-3

A: Firstly factor the Numerator and denominator and cancel the term and after that find limit.

Q: Use L'Hospital's Rule to evaluate the given limit

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4) State the limit definition of the derivahve. f'(x) =

A:

Q: Assume that lim (х, у) — (8, 6) f(x, y) = 2 and lim (х, у) — (8, 6) g(x, y) = 3 to find the limit.…

A:

Q: Use l'Hospital's Rule to calculate the exact value of the limit ) as x→ 0- Az) fX) = e -1 and g(x) =…

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: 26. Use the limit definition to compute

A:

Q: iN n?th coalculate the limit?

A:

Q: 8. ダ)→(2e) (x-りty

A:

Q: What is the limit?

A: The given function is: (x2 + 3x - 4) / (x2 - 1)Numerator = x2 + 3x - 4 = x2 + 4x - x - 4 = x(x + 4)…

Q: Give an example of a limit of the form 0/0 that convergesto 1 as x -> 0.

A: Given: Rx=fxgx is a function such that limx→0Rx is of the form 00 and converges to zero. To…

Q: 6. By considering different paths of approach, show that the following function has no limit as (x,…

A: given f(x,y)=5x2yx8+y2we need to show that the following function has no limit

Q: 4. Assuming the limit exists, explain what ∞0 means and explain why an ∞0 limit could be anything…

A: To discuss indeterminates and limits.

Q: What is the Reworded limit and continuity?

A: Given: limit and continuity

Q: What is the purpose of using one sided limit?

A: The main purpose of using one sided limit is that:We can check the behaviour of function and…

Q: what is the limit as x goes to 0 from the right of x^11x?

A: Refer to the function we need to calculate the limiting value of x from the right of x^11x.

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

A: We have to evaluate the following limit using L Hospital's rule: limx→0x2+xsinx L Hospitals rule…

Q: 9.) Explain why even though 2201 diveges, it has a finite limit of Ź 2n+1 n=1

A:

Q: Write the integral 1 1dx -1 x2 as a limit.

A: To write the given integral as a limit.

Q: what is the limit of x minus the square root of x, as x approaches infinity

A: Given,

Q: Evaluate the following limit: lim 10z²–4z =

A:

Q: what is the limit of x^4 plus x^5 as x approaches negative infinity?

A: Evaluate the limit of

Q: 1. Use the limit definition to evaluate ,(2 – 3x)dx.

A: The given integral is ∫-122-3xdx

Q: 7 Find a limit equal to V4x – 3dx. 3

A:

Q: what is the limit as x goes to infinity of (1-(4/7)^x)/(7-4(4/7)^x)?

A: Given function is

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.