3. Find the limits. (a) lim (x° +x² + x)' 101 %3D x -1 (x – 1)(x – 2) - (b) lim x2- x+ 1 (x - 1)(x – 2) (c) lim X -1+ 2 x+ 1 16 - (d) lim x4 x- 4 %3D 4. Let x+ 1, x< 1 |x – 1, x> 1 f(x) = - Find the limits that exist. (a) lim f(x) %3D X1- (b) lim f(x) = x1+ (c) lim f(x) = x 1

Q: (b) Find the following left- and right-hand limits at the vertical asymptote x = -6. Enter I for co,…

A:

Q: 1. Evaluate the following limits (if it exists) (a) lim X3 Vx+6-x (b) lim ズ→1 Vx-1+x2-x ズー3 xー1 2x…

A:

Q: 10. Find the value of the limit or state that it does not exist (DNE). a) lim f(x)= =(x)s u X -3

A: Given

Q: 2(x-1)* - y² Lex-1)* +2y (d) Show lim does not exist.

A: Limit exist

Q: 1- Evaluate the limit a-Lim(x/(x-1)-1/ Inx) x-1+ d- lim x+1/√2x²+x+1 x-→∞ b- lim [In(cos(x))]…

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Q: Match the values on the top with the given limit. A -o BO C 8/9 D +co 9 x2+12 x +9 lim 64 - x2 X- 8-…

A:

Q: find the limit of g(x) as x approaches the indicated value.

A: ltx→-25-x2gx=0As x tends to -2 denominator tends to 1 .    gx≠0 . gx&gt;0

Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

A:

Q: -1- x +3, if x -2 Calculate the following limits. Enter DNE if the limit does not exist. lim f(x) =…

A: Given : fx =-1-x + 3   if x&lt;-23                        if x=-22x+8                if x&gt;-2

Q: II. Apply the limit laws on the following: lim x→2 `x3-x 1. 2. lim (Vx/V) X-1 .cos x lim (*)(**+x²…

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: 1- Evaluate the limit a-Lim(x/(x-1) – 1/ Inx) b- lim [In(cos(x))]* c- 2-VX²+4 /sin'x x->1+ x >0 x>0…

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

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Q: 5) Find the indicated limit if it exists. Vx+4 – 2 a) lim x→0 8x' + 27 b) lim x→-1.5 2x+ 3

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Q: 1 Discuss the existence of the limit lim x 0 x2"

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Q: Find the following limits: Vx+3-1 i. x-2 x+2 lim 1 + x-1- \]x-1| ii. lim x2 +3x, Vx+-7 lim X→+co…

A:

Q: Find the limit. lim √√x+5 cos (x + π) X-IA O A. A. -√√5- B. √√5-T C. 0 O D. 1 OE. The limit does not…

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Q: Q1: Find the Limits of: Тan x 1- lim X+Sin x+VX 2- lim xo X+Sin x 3- lim vx2 + 1- Vx2-x

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Q: Find the limit. lim x+v-1 (x, y)- Vx+y-1

A: The given limit is of 0/0 form. In this type of limit problems, we try to remove 0 from the…

Q: 1- Evaluate the limit a-Limx²-4/(x²-x-2) X-2 b- lim [In(cos(x))]* c-2-(X²+4) ¹/2²/sin²x x-0 x →0

A: L'Hospital rule:- If a function is of the form p(x)q(x)   then if limx→a p(x)q(x)  is of 00 or ∞∞…

Q: 3x3 – x2 5x - - Evaluate lim Answer as a fraction in simplest x¬00 (2x – 1) · (x² – 4) - form or DNE…

A:

Q: 1. Find the limit, if it exists, or show that the limit does not exist. (a) lim xy cos(x - 2y) (x,y)…

A: This question is related to limit of several variables function

Q: B) Find the limits by using L.Hopital rule : x²–16 2. lim x→4 (Vx+5)-3

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: find the limit of g(x) as x approaches the indicated value.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Answer the question. 5, x<-1 x = -1 3-x, x2 +1, Wx-2+5, x2 2 2, Given f(x) = %3D -1< xs1 X 1<x<2…

A: Given function f(x)=1x+5, x&lt;-12, x=-13-x, -1&lt;x≤1x2+1, 1&lt;x&lt;2x-2+5, x≥2

Q: II. Apply the limit laws on the following: lim (Vx/VA) 2. X+1 cos x x5+ lim X-3 3. X-1

A:

Q: Find limit of lim メ-T(x*1) X-1 X-1 O a, 0 Ob. 1 00 d. None of these

A: Given the function limx→1xx−1   (x≠1)∵x≠1

Q: (4) Find the indicated limits, if they exist: Зх—12 (a) lim→4Jx-2 x²+3x-4 (b) lim→-4 +4x x²+4x 3 cos…

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Q: 2-メ Compite lim %3D Xラム z(T-X)

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Q: 2+4x 7. Prove lim = 2 using the e-ô definition of the limit. 3 %3D X-1

A: Hey, since there are multiple questions posted, we will answer first question of the first image. If…

Q: Evaluate the limits. |7x| f(æ) = { x # 0 x = 0 Enter DNE if the limit does not exist. a) lim f(x) =…

A: According to question,Given Function,fx = 7xxx≠00x=0

Q: (b) Find the following limits WITHOUT using the L'Hopital’s Rule. x²–4x lim x→0- |x| (i) (ii) 2tan?x…

A: Part i,Given,           limx→0-x2-4xx

Q: 8- x- x2 if x 3 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x)…

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Q: (1) Evaluate the indicated limits, if exist (x³ + 1) -x (а) lim r+0 V9 + x² (b) lim In I→1+ (c) lim…

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Q: 8) Find the limit (exact value) a) lim Vy - 3y – y ytoo tan ax b) lim- x→0 sin bx (a ±0,b± 0)

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Q: 1. a. Describe the level curves of the function f(x,y) = %3D x* + y b. Show that the limit lim (2,y)…

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Q: Find the limit. lim vx+11 cos (x + 3T) X-- 3T lim vx+11 cos (x + 3r) = →-3T Type an exact answer,…

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Q: Shone that lim g (x,yJ-p (0,0) does not exist,

A: According to the definition of limit, we have

Q: - Evaluate the limit a-Lim(x/(x-1) – 1/ Inx) b- lim [In(cos(x)) c-2-VX-+4 /sin'x x>1 x>0 d- lim x+1…

A: Limit values

Q: 1. Evaluate the limit: xy - y lim (x, y) → (1, 2) x² - x+2xy - 2y

A:

Q: 1. Find the limit if exists or show that the limit does not exist 1-cos(x+2y²) (x+2y2)2 (a) (b) lim…

A:

Q: (b) Find the following limits WITHOUT using the L'Hopital’s Rule. x² –4x lim x→0- ]x| (i) 2tan?x lim…

A: (1). From the given problem: limx→0-x2-4xx

Q: Find lim 4(x) (x) / X-0 x 2. Prove that B(m, n)

A: Limit of the bessel function

Q: 1.1. Find the limit or show that it does not exist. (a) lim (e + 2 cos 3x) (b) lim vx + ax - x2 + Bx…

A: Note:- In given problem, first problem already has two sub-parts. So, according to guidelines, we…

Q: Find the limit: lim f(x) as x approaches 0 of Kx2 - tan2 (mx)cos(mx)/x2     (m not =0)

A: Consider

Q: 1 11 lim X- 1 x2 + 9x – 10 Give your answer in exact form. If the limit does not exist, enter DNE.

A:

Q: 2. Evaluate the limits numerically. x-1 a) lim x-1 vx+3-2 x² +3x+2 b) lim x--1 x2-x-2 cos(x)-1 c)…

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Q: -x + 1, x > 0 3) Let f(x) = sin x -,x < 0' (a) Find left-hand and right-hand limits as "x"…

A: we have given f(x).  We have to find the left hand and right hand  limit.

Q: Q2.) Find the limit ( 10 lim 1- X- 0 X+ x cos x sin x cos x |x + 2| 2 - lim(x + 3) x-2 x + 2 lim sin…

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Q: Find the limit. cos(x) – 1 +x² .2 lim 2x4

A: NOTE: Refresh your page if you can't see any equations. . apply L'Hopital's rule

Q: x² – x + 1 1 - (c) lim x→1 x + 1 2 using definition of the functional limit

A: We can prove the statement as below using definition of limit

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.