a) Find two fuctions such that lim, +∞ ƒ (x) = ∞ lim, »0 g(x) = 0 = 00 but lim,->0∞ ƒ (x) – g(x) = 1

Q: 20. lim_ v3 – x x→3-

A: We have to find the limit

Q: 3-v49 B) Without using L'Hopital's rule, find: lim

A:

Q: Find limit of lim x-->0 of f(x)= (e3x-3x-1)/(4x^2

A: Given limx→0e3x-3x-14x2

Q: lim (In(x))½ ?

A:

Q: 10. Find the indicated limit. x²5x - 14 lim x→7 x - 7 Show any work necessary

A:

Q: lim In x X-→ 0+

A:

Q: f has domain of (-∞,–1)U(-1,2)U(2,00) lim f(x)=- %3D x→ -1" lim f(x)=- x→ -1* lim f(x)=3 x→2

A:

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

A: Solution:Givenlimx→∞ x-34x2+25To find the limit valueFormula:ab=ab

Q: Determine the law limit applied in solving lim 3 = 3. t-1 A. Limit of an identity B. Limit of a root…

A: Solution ) limit of a constant  limx→a b = b  limit of x tending to any value is value of the…

Q: Let Sz+8 3x +8 I-1 Approximate lim f(z) numerically and verify your answer graphically. If it does…

A:

Q: Which will best solve lim *-6x+9, х-3 x-3 O Derivatives O Limits of a function O Indeterminate forms…

A:

Q: V2x + 10 + Vx² – 5x + 10 lim - X→-1 x² + 1

A:

Q: Prove using formal definition. (a) lim x→0+ 1/x = ∞.

A: Draw the graph of the function .

Q: 10 Find lim x12s 3. X->- X -25 2 lim Jx +3 - 2 メ→」 O lim Sitx - -x 3. 1-X 2 X

A:

Q: Find the limit: Lim x->0  2 sin2 3x / 3x2

A: Given,         limx→02sin23x3x2

Q: Q.1 Evaluate the limit x-3 sin2x 1) lim(2x2 +x + 1) 2) lim 2-9 3) lim x-1 x-3 x2-x+1 4) lim x+00…

A: We have to find limit

Q: B. Find the limit. Зх— 1 5. lim х-1/3 9х2-1 x3- 1 6. lim х+1 х-1 Vx+5 -2 7. lim X→-1 х+1 Vx-1 4. lim…

A:

Q: Determine the limit at infinity. 4 22) lim 9 - (5/x²) X→-0

A: step 2 complete solution

Q: b- lim [In(cos(x))]= x->0

A: Given that:limx→0[ln(cosx)]x

Q: lim In (x°) x2

A: We have to evaluate the given limit.

Q: Determine the infinite limit. X 1 lim x4+ X - 4 -CO

A: We will plug x=4^+ in the expression first. We got 0 in denominator. So lets check by plugging…

Q: 4-VE Find the limit: lim→16 x-16

A: We need to evaluate the following limit limx→164-xx-16

Q: & Prove that lim I = 2 using the e-d-definition. Hint: Vr %3D

A: Given: To explain the given statement as follows, Here, prove that limx→4 x = 2.

Q: Find the limits

A: To evaluate the limit: lim1x2-4 (a). When x→2+. Evaluating the limit. limx→2+1x2-4=12+2-4=10+=∞…

Q: ® Find Lim X->2 x¥ _ 2x² - 8 x² - 4 (2 ,X +2 Lim 3X X→3 X- 3 -3 X+3 O Lim © Lim t- fo -) ,X EO X+2 2

A: "Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

A:

Q: 1. Find the limits. (Don't use L'hopital Rule) V2h+1-1 a. lim h-0 b. lim_(x – 3) -2| x--2 (x-2)

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: By L'Hopital's Rule, X-2 lim x→2 X²-1 1 1 lim. = x→2 2X 4

A: L’Hospital’s Rule: Suppose that  limx→a f(x)g(x)=00  OR  limx→a f(x)g(x)=±∞±∞ where a can be any…

Q: H-w in limits 3-3- 2.21 9 iaam ) Lim. 1- CosC2K) Sin (24) 2 - メャ3 2) Lim x2x -3 3) Lim (X+4}-16

A:

Q: 3* –1 lim V1+x -1,

A:

Q: Prove that limx->∞ f(x) =lim t->0+ f(1/t) and  limx->∞ f(x) =lim t->0- f(1/t)   if these…

A: We have to prove limx→∞fx=limt→0+f1t Take limx→∞fx Put t=1x when x→∞ then t→0 we get…

Q: 12-x-x 1- Prove that lim -7 %3D x-3 V6+x-3

A: our objective is to find the limit

Q: Fird the domain of f (x) = 2-Vx2-5 Solve lim x→-3 =? (Don't use L'hopital Rule) x+3

A:

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim X0 sin 2x x2-16 2. lim X+4 (VI+5)-3

A: *to find :- limits, using L-Hopital rule.

Q: a) lim- 1 3x +x+1 -x +5x b) lim f(x) where f(x)={ (4x xs2 3x x>2 sin 2x c) lim g(x) where 2+x < g(x)…

A: alimx→∞−x2+5x3x2+x+1Divide and multiply by x2limx→∞x2−x2+5xx2x23x2+x+1x2limx→∞−1+5x3+1x+1x2=−13

Q: • lim In (tanx) -Lーえ • Lim V9x* + ax 2 4x-1

A:

Q: Determine the infinite limit. lim 3 sec(x) x- (T/2)+ X 00 - 00

A: Given limx→π2+3xsecx, to find the limit

Q: Lim of √x, as x approaches to 4. Prove using epsilon delta deffinition

A:

Q: • Find the limits of 2+x-V2 • lim Vx -3 • lim X→9 x-9 x³+1 lim X--1 x+1 V5+x -V5-x • lim x-0…

A:

Q: 3 - – If lim f(x) = 3.5 and lim,-2+ f(x) = 6. 5 , the function has a double sided %3D x→2- limit or…

A: Given,          limx→2-fx=3.5 and limx→2+fx=6.5We know that,           Condition of double sided…

Q: 2. If lim x, = 1 and lim yn = 0, then it is possible to formally prove that lim(x, – Yn) = 1.

A: (Solving the 2nd question as per our guidelines) Solution of 2: The statement is "If lim xn=1 and…

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

A:

Q: Prove that lim x cos 4 = 0. X-0 -1 s cos(4/x)s 1 = -x s cos(4/x) s x*. since lim (-x*) = x-0 and lim…

A:

Q: 2. Evaluate the limit: 1000 lim TC lim -7)2 (8-x)3 x→8+ x+7-

A: The left-side of the limit of a function at a point is the value of the function when the value of…

Q: V5x+6-4 1. Use L'Hopital's rule to evaluate the limit: lim- x-2

A:

Q: Use basic techniques to find the limits. 8. lim(-7) X-3 9. lim (x³ + 2x) X→-1 10. lim cos x

A:

Q: x-3x+5 by X-0 4x2+2x+3 10. Find the limit: lim means of the L'Hopital Rule

A:

Q: EXAMPLE 5 A Limit That Does Not Exist numerically. Investigate lim sin graphically and

A:

Q: Find the limit of sec x as x approaches x lim sec x x->0

A: Topic = Limits

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…

A:

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.