Let f(x) be a piecewise function defined by x+1 if x < 0 f(x) = {5 if 0 < x < 2 x² –1 if x > 2 Find lim f(x). X-1+ А) 5 В) 2 C) the limit does not exist

Q: If the fucntion f is undefined at x then lim f(x) does not exist. = c, C, FALSE O TRUE

A: Given- If the function fis undefined at x=c then limx→cfx does not exist. To Check- If the above…

Q: 3 Find the limit: lim t 3 et – 1 - (Enter undefined if the limit does not exist.)

A:

Q: 1. Show the limit lim (r.y) ›(0,0) I 6 +y² does not exist

A:

Q: Let f(x)={−2x+2  x≠1               {2   x=1. What is f(1)? If f(1) does not exist, type: 99999 What…

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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: Use the definition of limits at infinity to prove the limit

A: Definition of limits helps to find the limit of the function. A value is said to be the limit of…

Q: Show the limit does not exist. lim (1,y)→(0,0) x6 + y²

A:

Q: 3. Use the epsilon - delta definition to prove that the limit is lim Vx x-0 371 when

A: To use epsilon delta definition to show that the below limit is 0. limx→0x3=0

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

A:

Q: and If lim f(x) = lim g(x) = +o and flx) =1 and gtxl = e, what is the limit of the division of !!…

A: As given limit is infinitely by infinity form so use L'hopital's rule and substitute the given…

Q: 10. Let a be a positive constant. Evaluate lim x(a/x – 1) if the limit exists. If the limit does not…

A: limx→af(x) does not exist. The idea is that there is no number that f(x) gets arbitrarily close to…

Q: Let f(x)={−2x+2   x≠1               {−5         x=1. What is f(1)? If f(1) does not exist, type:…

A: Given,

Q: Prove that lim (x,y)(0,0) x² + y² does not exist by considering the limit along the x-axis.

A: Given: lim(x, y)→(0,0)xx2+y2

Q: Let f(x) = 2x² + 2x + 3. According to the definition, f'(x) = lim h→0 (Enter the limit in reduced…

A: the soluton is following.

Q: Q4 Evaluate the limit lim (x.y)-(0,0) 3x2+y xy cos y if it exist. If not, show that the limit does…

A: In this problem we compute the limit along x axis and along the line y=x .If these two limits are…

Q: (a) Show that the limit x*ycosy lim 12 (xy)→(0.0) 2x* +y² does not exist.

A: Student has specifically asked for the solution to question (a).

Q: Let y = f(x) be a continuous function. If ƒ has a local maximum or minimum value at x = a, then the…

A: Let y=f(x) be a continuous function. If f has a local maximum or minimum at x=a,then the limit…

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: Show that the following limit does not exist. ху lim (x. y)-(0, 0) 3x2 +2y2

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Q: Show that the limit does not exist. (x + y)² lim (1,y)→(0,0) x² + y²

A:

Q: 5) a) If a > 0, compute lim a¯*. b) Which approaches its limit faster as x→», y=2* or y=x²?

A:

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

A:

Q: Let f(x, y) = xy /(x 2 + y2). Show that f(x, y) approaches zero along the x- and y-axes. Then prove…

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

Q: 2

A: According to the given information, it is required to prove the limit using epsilon delta…

Q: Use the two-path test to prove that the following limit does not exist. y-2x2 lim y+x (x.y)-(0,0)

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Q: 2. Use the definition of the limit to prove that lim (r+2y – 1) = 1. (1,9)¬(0,1)

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Q: lim x3 In(x) X→0+ to

A:

Q: Show that the limit does not exist: (y² + x – 1)² - lim (x,y)→(1,0) (x – 1)2 + y4

A:

Q: 1. Show that the limit lim (2,y)(0,0) In(1 – a2)+ y* x² + y4 does not exist.

A:

Q: Use the definition of the limit of a function of two variables to verify the limit.

A: We have to verify the limit: limx, y→1, 0x=1 According to limit value, x, y→1, 0 therefore, x=1y=0

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

A:

Q: 9 -x2 if x 1 .What value of c makes g(x) continuous at x = 1? Show all conclusions. 2 Vx-4 Using…

A: For a function to be continuos, the left hand limit should be equal to the right hand limit.…

Q: Prove the limit. Using the precise definition of a limit. lim x approaches 0 xsinx(1/x)=0

A: To prove:

Q: [ 2 Let f(x) x – x2 if x 3 - Calculate the following limits. Enter "DNE" if the limit does not…

A:

Q: Evaluate the limit if it exists, or show that it doesn't exist: xyz lim (x,y,z)→(0,0,0) [x² + y² +…

A:

Q: A function f has a removable discontinuity at x = c if limf(x) exists by f is not continuous at x =…

A: Here, the given function is: f(x)=x-2|x|-2 So, function is not defined at x=2,-2

Q: Evaluate the limit below. 1 lim (x,y)→(0,0) 1-x2-y?

A: limx, y→0, 011-x2-y2

Q: 4. Use the € & definition of limit to show that lim (2z+3i) = 2 + 5i. z+1+i

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: 2) Show that the limit exists : 3x3 ,3) lim (x.y.z)-(0,0,0) x2 +y² + z2

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Q: 12 Show that the following limits do not exist. 1 lim X0x (a) (x > 0), 4,

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Q: Let f(x)={2−x−x2ifx≤12x−3if 1 Calculate the following limits. Enter "DNE" if the limit does not…

A: The given function is , f(x)=2-x-x2   if x≤12x-3       if x&gt;1 we have to Calculate the following…

Q: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: 4] [2M] Determine whether the limit exist in R for lim xsin(1/x²), (x# 0). x→0

A: Zero

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: af is lim if f(x) x2 he limit does not exist.

A: Please refer to the image below

Q: Find Limit Using Squeeze Theorem: 3. If 2x s g(x) s x* – x² + 2 for all x, find lim g(x).

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Q: 2. Find the limit using Squeeze theorem 1 lim,2|a – 2| sin( `x – 2

A: Given: limx→2x-2sin1x-2

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

A:

Q: |x| does not exist. Show that the limit lim x 0 X

A: Given: limx→0xx