5.8. Show that if lim f(z) = wo, then lim f(2)| = |wo|.

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

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Q: b* – 1 Show numerically that for b = 2 and b = 4, lim x→0 appears to equal In 2 and In 4,…

A: Given limit:

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

A:

Q: The value of the limit 3 lim (1- z/2 is equal to O e-3/2 O e3/2 O e2/3 O 1 The limit does not exist

A: Given: The limit limz→∞1-3zz2.

Q: b* – 1 Show numerically that for b =3 and b = 5, lim appears to equal In 3 and In 5, respectively.

A: Here given

Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

A:

Q: b* – 1 Show numerically that for b = 3 and b = 5, lim аppears to equal In 3 and In 5, respectively.

A: Given : limx→0bx−1x

Q: lim V3x² – 6 X-2

A: The given problem is,           limx→23x2-6 Here the function is continuous and defined at x=2, so…

Q: 3x lim x→0 x2 + 2x

A:

Q: show that : Lim h→0  h / √5h + 4 − 2 =4/5

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Q: Evalate the limit 6. lim (e + x)²/x

A:

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: 5. lim x-0 e2x-1

A: LetL=limx→ 0xe2x-1Plug in the value x=0L=0e2(0)-1L=01-1L=00Therefore Apply L Hospital ruleL=limx→…

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

A:

Q: S* 56sin(t")dt Evaluate the limit lim .8

A:

Q: . Suppose a state's income tax code states that tax liability is 12% on the first $20,000 of taxable…

A:

Q: (4) Consider the function + 3bx + 262 if x 1 For which value(s) of b does lim f(x) exist? Justify…

A: Given: fx=x2+3bx+2b2             if x<1 fx=x-1                             if x≥1 limx→1fx…

Q: 1 is equal to cOs x - The value of the limit lim x2

A:

Q: Suppose a state's income tax code states that tax liability is 18% on the first $19,500 of taxable…

A: The tax function,   T(x)=a+0.18xx≤19,500b+0.14x-19,500x>19,500

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

A: We can solve part in the following steps.

Q: 3. Show that if x > 0 for all n e N, then lim(x,) = 0 if and only if lim(1/x,) = +oo.

A: Consider the given information. xn>0 and limxn=0 Now, use the limit definition of the sequence.…

Q: (7) ifa lim has a point that the equalio- prove PCz,y) is above L and only if 3x +2y >4

A:

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

A:

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

A:

Q: 1 Use a plot of f (x) = 4 Vx - 2 to estimate lim f(x) 4 メ→4 | numerically.

A: Given: f(x)=1x−2−4x−4Estimate:limx→4f(x)=?Graphically  and  Numericallly

Q: 3. Is lim f(x) always equal to f(c)?

A: Is limx→cfx always equal to fc The given statement is not necessarily true.

Q: 2. lim (e* +3x)

A:

Q: 6. Use the e, 8 definition to show that lim,2 x + 1 x+ 3 emlin

A:

Q: Determine the following limits at infinity. 10 lim a5 + *+

A: Given, limx→∞a5+1x+10x2b

Q: From the function H defined by sections a) Estimate the following limits: lim x→1/2h(x), lim…

A:

Q: lim -2)2 x-2 x2-4 3.)

A:

Q: Find the limit of the equation.

A: Evaluate the limit

Q: 5. Use the concept of limits to solve for the following problem iz3 – 1 lim z-1 z + i

A:

Q: 5.3. Show that when a limit of a function f(z) exists at a point 2o, it is unique.

A:

Q: 1. Use a table of values to estimate the limit correctly to the nearest hundredth. x' - 3x? +2x –- 6…

A: Please see the answer below.

Q: 1 Ask for the answer to lim x (1 – e * ).

A:

Q: 2. Find the following limits. Do (a) and (b) without a calculator and (c) and (d) with a calculator…

A: We have limx→0x-4x+4=limx→0x-4limx→0x+4=0-44=-42=-2

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

A:

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

A:

Q: Find the limits limx→e+(ln x)1/(x-e)

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

A:

Q: 2. Construct a table of values to investigate the following limits. 2r +1 lim a. 42 I-3 I+3 if z1

A: This is a problem related to the limit and continuity. Limit of the function is exist if right hand…

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

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Q: + 1for all positive x-values, then what is lim f(x)? X+ 4

A:

Q: 10. Find the value of the limit or state that it does not exist c) lim f(x) = X2"

A:

Q: Evaluate the following limit.         lim           ln 3sqrtxy (x,y)→(27,e^9)

A: Given,         limx,y→27,e9ln3xy

Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

A:

Q: 1. lim (3x + 4)

A: