Problem II: Determine which of the following limits exist, and find the limits which do exist. a) lim *'+ (1.9)-H0,0) X* + y² x' + 4.xy² + 4y* x' + 4y* b) lim (х.у)-қ0,0)

Q: 1 Find lim +3 using limit rules. 2.

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Q: Find the limits

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

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Q: 1) Show that the limit doesn't exist 3x2 1) (x.y)(0,0) x2 + y² lim 2) (x.y 3) lim ysinx 4) lim

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Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x,y)→(0,0) x²+y2

A: To show that the limit of a multivariable function does not exist,…

Q: . lim (3 – 2e

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Q: How does the sandwich theorem enable us to calculate a variety of limits?

A: Sandwich theorem: Consider 3 function f(x),gx,hx such that fx≤gx≤hx. Also, assume that limx→cf(x)=L…

Q: lim 2tan (2.x) 3n 4

A: This is a basic limit problem

Q: Problem 4, Use L'Hopital' Rule to evaluate the following limits 1. lim,-1»; - sinte) 2. limr+ x x→∞…

A: Solving 3

Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

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Q: г — 5 lim I-5 x2 – 5x

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Q: 8 - x- x2 if x 4 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

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Q: 12, Show that the following limits do not exist. (а) lim 1 (x > 0), (b) lim (x > 0), x-0x2 x-0 Vx…

A: Given: d) limx→0sin1x2 to prove limit does not exist.

Q: Estimate the limit numerically. 3x² +270x+5 lim 2x+15 + oo

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

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Q: Compute the limits that exist. lim x---0, x2 + 3x/x

A: Given: limx→0x2+3xx

Q: We want to find the limit lim os(2æ) – cos(7x) - x2

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Q: 1 (i) lim

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Q: lim x" x→0+

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Q: iv. lim x' -2x² X -00 v. lim 3x – Vx* – 2x +3 lim I-0 x vi.

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Q: 4 Find the limit: lim sin(x) (Enter undefined if the limit does not exist.)

A: The given limit limx→04x-4sin(x)

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

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Q: X- Zx +3x+2 lim

A: Solution of question as follows

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: Show the limit does not exist by choosing two paths to the origin whose limits L1 and L2 are not the…

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Q: Choose the limit that would NOT use l'hopital's rule. 1³ – 1 lim I →1 1² – 1 (=* – 1) (=² – 1) * lim…

A: We can find the answer as given below

Q: x² - y? lim ) - (0, 0) х? + у? y

A: Here we have to show that, lim(x,y)→(0,0) x2-y2x2+y2

Q: QUESTION 2 Prove using the definition of a limit that lim x² + y2 -y = 4. >

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Q: Show that the limit doesn't exis 3x2 1) (x,y)→(0,0) x² + y² lim 2) (х,у

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Q: if x — 4 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x→ –…

A: a)

Q: When trying to explain an infinite limit. What does it mean to say that: lim as x approaches 0…

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Q: By considering different paths of approach, show that the limit lim (1,y)→(0,0) rª + y² does not…

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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: 5. Find the limit or show that it does not exist. sin(x – 1) lim x→1 x´ +x –2 2

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

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Q: Compute this limit to infinity   limx→∞ of (7x^3 + 2020x+ 4)/(πx^3+ 18x^2+ 12)

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Q: Problem 8. Find the limit lim (1- 2x)/ if it exists. If you use the Hopital's Rule, be sure to…

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Q: 1b. Use L'Hopital's Rule to find the Limit:    lim      2tanx/sec2x x->pi/2

A: To find the limit

Q: . Suppose f(т/3) — 5, f (т/3) — —3,а sin(3та) 2->0 sin(5Tx) . Find the limit: lim

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Q: x2 + 2x + 1 lim x--2 x2 + x +1

A: There is no need for L hospital as the limit can be evaluated directly.

Q: Find the limits limx→0+x tan (π/2 - x)

A: Given that, f(x)=x tan (π/2 - x) We have to find, limx→0+xtanπ2-x

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

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Q: 5. Find the limit. lim (Inx)2

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

A: Given:

Q: 6 -- if a - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

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Q: 7. Show that the limit does not exist by approaching (0,0) lim .2 ,2 + y- (x, y) (0,0)

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Q: Show that the_limit exists : 2x²siny 2), lim (x,y)→(0,0) 2x² + y²

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Q: Find the limit: limx→0​ x3sin(1/3x​3)

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Q: -x e lim In(1+4e-x)

A: The answer is 1/4

Q: 5) Find the indicated limit if it exist. а) lim X-2 3- Vx+ 7 2 - x x' +1 b) lim x-- x+1

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.