_15. What is lim f(x)? X-4 A. 0 В.1 С.2 D. Does Not Exist

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

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Q: Let n be a positive integer. For which n are the two infinite one-sided limits limx→0±1/xn^n equal?

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Q: 1. Determine if the following limits exist: x² + y5 lim (x,y) (0,0) 1 - cos(x) + y4 (a)

A: Sol: Part (a) limx, y→0, 0x2+y51-cosx+y4Find two different paths to approach the point that gives…

Q: Solve for the limit: lim \belowx → 3 x2-9 O a. 1. 54 c. 6. 1 54 O d. 1/9

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Q: 4) Find the following limit or show that it does not exist. sin(ry) a) lim (1,y) (0,2) b) lim…

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Q: 2. Compute the following limits at infinity and give reasons for your answers. 1 a) lim b) lim 10 4x…

A: 2(g) Given limit is : limx→∞6x2-7x+14x3-7 To find the value of the limit.

Q: 6 — х — а? if x 1 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

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Q: Evaluate the limits: lim (cosx)cor*x 13. Ans: e12

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: I. Evaluate the following limits. x sinh x 1. lim x-40 cos 3x – 1

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Q: lim (x 1/2 ln x) X→∞

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Q: lim 4 sin(x + n) + 3

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

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

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Q: 3. Compute ahi-fin Lireh-fi for the following functions: and lim h40 a. f (x) = sin x

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Q: V4 + x – V4 – x lim x-0 O 1/2 О 113 O 1/4 O 1/5

A: To solvelimx→0(4+x-4-xx)

Q: (c) Find the following limits WITHOUT using the L’Hopital's Rule. -5x2-8 lim x→+∞ 2x+3 (i) Зx+1-сos…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 2. Calculate the following limits. Justify your answer. L'Hopital's rule Rule ) (without using 2x +1…

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Q: Find the value of the following limits: 5y 1-limy→o tan 10y 2-limx-0 6x cot3x 7x²+8x 3-limx-0 4x²…

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Q: 8. Evaluate the limits by previous methods or by L'Hospital's Rule, if applicable: 4x3 +3x 4x b) lim…

A: We have to find limit

Q: 4-IS. 2-x s Mx) s 2Cos(x) for all x then find: lim f(x)

A: It is an application of sandwich principle of limit

Q: 1. Evaluate the following limits (DO NOT use L'Hopital's Rule): V7+ 2x - 3 (a) lim 1-r 42021 +3 (b)…

A: 1. (a) limx→1 7+2x-31-x

Q: 2) If x3 s f(x) sx for x in [-1,1), find lim f(x) if it exists. x-0 A) 0 B) Does not exist C) -1 D)…

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Q: 2 Show that the following limit does not exist. lim Ty Cos y (r.9)-(0.0) 3r+ y²

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Q: Use the Squeeze Theorem to prove lim = 0. x00 x+ e- For x 0, since 0 < e* <1, we have

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Q: 2-メ Compite lim %3D Xラム z(T-X)

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Q: 5. Apply L'Hopital's rule to determine the limits of the function. y = lim e"(x – a² + 9)

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Q: Q4)A) Find the following limits (for two only). x+1 1. limy--17-x-2 1-VE 2. limy-1 1-x 2x 3. lim--0…

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Q: Q3. Compute the following limits if they exist. SEC x – 1 (а) lim x→0- sin x (b) lim x→0 x tan x 2 -…

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Q: 6. Figure out the following limits without applying L'Hopital Rule. sin(r- 4) V2r -1-1 b. lim (2²…

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Q: - x – x2 if x 2 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

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Q: cosx * sin? (3x) 2 2. lim x→0 x2

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Q: 6 Compule the following limit lim glx) whene X-0 9 = (05 (2x) x९ o ( ৪-४, ४>0 where

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Q: What is the value of a if the limit of the function is 3, given by еах —1-ах lim X→0 ex2. = 3? -cos…

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Q: (a) Compute the following limits: (i) lim **+x²+x+1 x2-1 sec-1(vZ+h)-sec-1/2 (ii) lim h→0 h

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

Q: 2 — х — г? if x 5 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: Here we will find the given limits,

Q: 6ln (1+x) lim х>0 2е3х—2secx

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Q: x² + x 1. lim x++∞ e²x + Inx 2. lim (sech 2x) esch x² +0+x

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Q: 4. Find the following limits or determine that they do not exist: 1+1/x a. lim,-0 1+1/x² 1+1/x? b.…

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Q: 1 lim x sin x x2 x→0 O 1/5 O 1/7 О 16

A: Given, limx→01x sinx-1x2

Q: 1. Prove the following limits x 4y4 G) lim (x,y) (0,0) (x²+y4)3 = Does not exist

A: Solution is given below:

Q: S 10 – x – a? if x 1 Calculate the following limits. Enter "DNE" if the limit does not exist. 2x +…

A: The given function is f(x)=10-x-x2if x≤12x+6if x&gt;1 We have to calculate,  a) limx→1-f(x)=?b)…

Q: 11) lim sin²y Y→TT 1+cosy

A: sin2y=1-cos2ya2-b2=(a+b)(a-b)

Q: S (2t)*dt lim x→ =? х* — 1

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Q: By using The definilion of the D Lim x (X+1)= o 2) Lin x Cos

A: Given: 1)limx→0x(x2+1)=02)limx→0x cos1x=0

Q: (e) lim e* ニD 2. (g) lim -X- www. indetern

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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: I. Evaluate the following limits. x sinh x 1. lim x-0 cos 3x -1

A: Since you have asked multiple questions, as per Bartleby guideline, we are allowed to answer only…

Q: T is discontinuous at -1 because lim f(x) as x--> -1 does not exist. * %23 .7. 5. %23

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Q: 2. Determine the value of the following limit along all paths through the origin for which x + -2y.…

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Q: (i) Prove that Lim Vent +1 1 1 + + + /2n²+n] ... V2n2+2

A: Given that, g(x)=limn→∞12n2+1+12n2+2+....+12n2+n from sandwich theoram we can say if f(x)≤g(x)≤h(x),…

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.