A function f(x) is said to have a jump discontinuity at r = a if: 1. lim f(x) exists. 2. lim f(z) exists. 3. The left and right limits are not equal. 3x – 7 if z < 7 Let f(x) = if r>7 z+6 Show that f(æ) has a jump discontinuity at a = 7 by calculating the limits from the left and right at x = 7. lim f(x) = lim f(x) =

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A: Given limx→c f(x) does not exist because the left-hand and right - hand limit have different values.

Q: 1) Find the Limit lim/→0 3x²h-7th+h h

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Q: Use l'Hôpital's Rule to evaluate the limit. .3 8x +7 2, lim X- 1 X1 O A. 11 O B. 19 C. O C. - 16 D.…

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Q: 2. Compute the following limits at infinity and give reasons for your answers. 1 a) lim b) lim I00…

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Q: Q4)A) Find the following limits (for two only). x+1 1. limx→-1 х2-х-2 1-Vx 2. limx→1 1-x 2х 3.…

A: Part 1,Given,           limx→-1x+1x2-x-2

Q: Find the limit, if it exists.

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Q: Find the limit (if it exists).

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Q: Use l’Hôpital’s rule to find the limits

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Q: Find a & that works for & = 0.1 for the following limit. lim 6x + 7 = 13 x1

A: The limit is given by limx→16x+7 = 13 To evaluate: The value of a δ that works for ε=0.1

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Q: (3) Find the limit if it exists. - ay? (a) lim (1.y)-(0,0) r2 + y?

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Q: 3x 8 if x 7 x +5 Show that f() has a jump discontinuity at x = 7 by calculating the limits from the…

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Q: 3. Can f (x) approach a limit as x → c if f(c) is undefined? If so,

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Q: 4-ху Find lim (x,y)¬(2,1) x²+3y2 if it exists, or show that the limit does not exist.

A: limx, y→2, 14-xyx2+3y2Plug in the value x, y=2, 1=4-2· 122+3· 12=27

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Q: 2. Use the paths x = y and x = 0 to verify the limit. lim (x.y)-(0,0) x2+y²,

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Q: Recall that J x+ 4 |x +4| = ((x+4) X <-4. Therefore, we will need to check the limits when…

A: NOTE: Refresh your page if you can't see any equations. . as we know,

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Q: 3, Use the definition of limit (E & 8) to show that lim (2.x+iy)-4i, where z=x+ iy. 21

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Q: Use the &-8 definition of e limit to prove lim+1 =2. x→5 5 nd the ɛ value when &=0.001.

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A: We will find the limit as following.

Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

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Q: 6x – 6 if a 4 Show that f(x) has a jump discontinuity at a = 4 by calculating the limits from the…

A: Let fx=6x-6if x&lt;41x+4if x≥4 To show that f(x) has a jump discontinuity at x = 4.

Q: A For the limit lim (x-3x + 4) = 6 illustrate Definition 2 by finding values of d that correspond to…

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A: Limit:      x→e+limln x(x-e)=h→0limln (e+h)(e+h-e)

Q: 1. Calculate the limit numerically. lim(x + 11) x→2

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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: Find the limit (if it exists). (If an answer does not exist, enter DNE.) Sx2 - 4x + 6, X < 3 lim…

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Q: Use l’Hôpital’s rule to find the limits

A: Since, we have to find the limits of the function given below:-limh→0 eh-(1+h)h2 -(i)

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.