3. is a type of discontinuity when the lim and lim f(x) = M where L# M and either f(a) does not exist or lim f(x) : X-a*+ X-a f(a).

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

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Q: Find Limit Using Squeeze Theorem 2. If 2x – 2 < f (x) < x² – 4x + 3 for x 2 0, find lim f (x). - x→1

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Q: Find the limits limx→0+{1 + 1/x}x

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Q: 2) Show that the_lim. 1) xy2 lim (x,y)→(0,0) x² +y²

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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: Suppose f(– 1) = 0 g( - 1) = 0 f'(– 1) = 5 g'(– 1) = 4 and all functions are continuous. lim…

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

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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: 9. Given that limx→3 f(x) = 2 and limx→3 g(x) = −5 compute the following limits: (a) limx→3 2f(x)…

A: Given that limx→3f(x)=2 and limx→3g(x)=-5

Q: Suppose that on the interval (2,5) f(x) less than or equal to g (x) less or equal to h (x) and Lim…

A: We have the following information.

Q: Show that lim (x,y)→(0,0) 16x4+9y12 4x²+3y6 does not exist.

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Q: 2. Use the definition of the appropriate limit to show (a) limr→∞(2x² + 4x – 1)/(3r³ + 1) 0. - (b)…

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Q: Find the limits x² - 7x lim X-o X + 1

A: Given: limx→∞x2-7xx+1

Q: Q2 e valuat of the fallowing 2. ☺ lim L(x +3)t -16] xーース ☺ lim -25 X+5 メー5 lim |-X 3+X 9. X-3 メー] O…

A: To evaluate the given limits.

Q: Verify the limits in a given equation below. (2х-4)2 lim X→3 x+1

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Q: Evaluate the limit using L'Hospital's rule: x13* lim x→0 13* – 1 -

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Q: 5. Evaluate the limit: Vx +1 lim x→1 4x -4

A: Limit at a point exists if left-handed and right-handed limits exist and they are equal. Left-handed…

Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: 4. Do you agree with the following statement? When a function f is continuous at a number a, then it…

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Q: If 3x s f(x) sx +2 for 0sxs 2, evaluate lim f(x).

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Q: Calculate the following limits x2+4x-12 а) lim x-2 b) lim Vx +1 In(x+ 1) |x-21 X→ー1

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Q: suppose f,g an d h are functions which g(x)<=f(x) <=h(x) ,for all x in an open interval containing a…

A: No. For the given continuous open interval domain, the limit of f(x) does not exist.

Q: i. Calculate the following limit: 2x|x – 1| lim - x-1 x-1 ii. Determine the limit of f(x) when x…

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Q: 5. Show that x³y³ lim (x,y) →(0,0) 2x¹2 + 3y4 does not exist.

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Q: 2x-1 2. lim X-2 \3x+4,

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Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: Show that 16x4+9y12 lim (x,y)→(0,0) 4x²+3y6 does not exist.

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

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Q: lim x3 In(x) X→0+ to

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Q: From the graph: (x) is discontinuous at x= 3 because of (a) Lim f(x) = f(3) (b) Lim f(x) doesn't…

A: According to graph at x = 3

Q: -. Calculate each of the following limits, or explain why it does not converge. limx - 3 (x-2) /…

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Q: 9. Determine the exact answer for the following limit analytically: Vx+1-2 lim- x-3

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Q: . What is the point discontinuity of the x² – 1 lim x→-1 x +E 1

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Q: show that lim(x,y)→(0,0) (x^3+xy^3/x^4+y^2) does not exist.

A: We will see that along y=mx2 path limit does not exist which means limit does not exist.

Q: (2) Suppose that a function f(x) is defined for all real values x except x* x,, then lim f(x) does…

A: For limit to be exist at a point, left hand side and right hand side values of function should be…

Q: 44. Prove that if lim f(x)= L #0 and lim g(x)= 0, then the limit lim 8(x) does not exist.

A: Given: limx→cf(x)=L≠0 and limx→cg(x)=0 To Show- limx→cf(x)g(x) doesnot exist. Theorem- if limx→au(x)…

Q: Find the limit. x* – 1 - lim x→0+ In (x) +x – 1 п lim ( 1+ n

A: These question is based on Limits.

Q: Use continuity to evaluate the limit. lim In(2 + V1 + x)

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Q: show that L’Hôpital’s Rule is applicable to the limit as x →±∞and evaluate

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Q: —ах+6 if x2-1 Let f(x)=< For what value of a does 2x2 +ах ifx<-1 lim f(x) exist? x--1

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Q: Determine the limit of the following: yA y = f(x) | 1. lim f(x) = %3D - 2. lim f(x) = X-1- x- 2- 3.…

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Q: If there is no single value that is approached by f(x) as x approaches a, then lim f(x) does not X→a…

A: If there is no single Value that is approached by f(x) as x approaches a,then limit of f(x) as x…

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: 3. Compute the limit algebraically Vx +3x2 lim 6x 1

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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: Find the following limits analytically or state that they do not exist. 2x+1 3. lim- x+0 x2+1

A: Given:limx→02x+1x2+1

Q: Determine the following limits at infinity. f1x2 xSo g1x2 lim if f1x2 S 100,000 and g1x2 S 00 as x S…

A: Given information: The function f(x) approaches 100,000 and g(x) approaches infinity as x approaches…

Q: 6. Explain why the limits lim f(x+h) – f(x) and lim f(2) – f(x) h Z-X are each initially in the form…

A: Given that the limits are limh→0fx+h-fxh and limz→xfz-fxz-x.

Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

Q: 3x – 1, if x 8 | Let f(x) = { 5 x+9 Show that f(x) has a jump discontinuity at x = 8 by calculating…

A: