18) Find lim f(x) %3D X 2 - A) – B) 2 00 C) 1 D) 4

Q: is continuos if lim f(z) =f(z,) ylgn O ihi O

A: Continuity: A function f(z) is said to be continuous if all the three of the following statements…

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

A:

Q: If f(x, y) approaches 1 as (x, y) approaches (0, 0) along the path y = mx, where m is any real…

A: To check whether the given statement is true or false.

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

A:

Q: Find the limit lim (z + 7i)?. z→2-5i

A: Consider limz→2-5iz+7i2 = 2-5i+7i2= 2+2i2= (2)2+(2i)2+2(2)(2i)= 4+4i2+8i= 4+4(-1)+8i= 4-4+8i= 8i

Q: Prove that lim r(x)= where m = 0, 1, 2, 3. .. II

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Q: What is lim f(z) z→1 9(2) given f(x) = e2" and g(x) 3x2 – 3x + 6 ?

A:

Q: Q: Prove ha中 Lim x" an %3D

A: we have to prove that the following

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

A:

Q: Show: ( (|fl2 – €)² < lim sup E If (n) < (I|fl2 + e)² , Where ƒ E C(R | Z; , c) n=-N

A:

Q: O Find lim (X,Y)→ LD,0) **+3y* or show it DNE.

A:

Q: ,3 Find lim (x,y)→(0,0) x² + y² °

A:

Q: Prove that both (a) lim inf y, 2 lim inf r, (b) lim sup y, < lim sup r„.

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Q: If lim, » 1512i (z2 + 30z) = x + iy, what is the value of a

A:

Q: Show that lim (2,v)>(0,0) **+y D0.

A:

Q: Use the precise definition (i.e. the ɛ, d definition) to prove that lim, →1 x2 – 3x + 5 = 3

A:

Q: If A = lim ("C " C " C_ " C ……." C )m(a+1) then A² is equal to

A:

Q: By considering different paths of approach, show that the limits in Exercises 15 and 16 do not…

A: Since you have asked multiple questions, as per policy,  only the first part is answered. In case…

Q: Prove that lim r(x) = 0 where m = 0, 1, 2, 3. ...

A:

Q: Which property of f(x) = x' allows us to conclude that lim x = 8? x+2

A: f(x) =x3

Q: Use the e-d definition to show that lim /a = 2. a-b (Hint: Vā – V6 =

A:

Q: . Use the sandwich theorem sin x (a) lim Vx 400

A: The given expression is: limx→∞sin xx

Q: Prove the following. (b) lim( Vn² +1 – n ") = 0 - (c) lim Vn? n) = } 1 2 ||

A: Prove the following limits

Q: B. Evaluate the Limit: 1. lim 3x z + yxcos(Tx – nz) = %3D (x.y,2)-(2,1,-1)

A: Solving question no.1

Q: Use an appropriate definition to prove the following limits. g³ – 16x4 = 1 x + 2 9x² + 4 (а) lim…

A: We prove the given limits: limx→5+x+2x2-25=∞ limx→∞x5-16x4x5+4x2=1 limx→-∞9x2+4x+2=-3

Q: 4e' + 3e-i lim t→∞ 5e' + 2e

A: NOTE: Refresh your page if you can't see any equations. . divide the numerator and denominator by

Q: Exercise 6. Find the limits. 1 dx. 1+ x2n lim

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Q: a). Evalieteo lim foca+la -4 X-2 b). f(x){ de?+72, xこ 3x2+3d9x > a Contir at evesy ?

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Q: The value of lim (trorozac) 2 (1² 1px (ozoz-ozoz) 6202 (17073— 170741) 7 is equal to

A: The property of exponents is anam=an-m. The property of exponents when the exponents are in…

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: [4] (a) Show that lim (xa)-(0,0) 2x+y? y-mx, or along any parabola y= exists and it's approaches to…

A:

Q: Use an appropriate definition to prove the following limits. x³ – 16x* = 1 I+0 r°+ 4x² x +2 V9x2 + 4…

A: This is a problem of limit . Based on the formula and concept we will answer the question.

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

A:

Q: 2 lim w ln( 1 3w

A: Given:      limω→∞ω ln1-23ω     =limω→∞ln1-23ω1ω   Apply L'Hopital's rule        If limx→af(x)g(x)=0…

Q: Use the Squeeze Theorem to evaluate [2 lim cCs X x +3

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Q: 2. The value of lim is (z.v)-(0,0) Vr² + y? (b) 1 a) 0 (c) 2 (d) does not exist

A:

Q: ow that lim (x,y) → (0,0) 4 3x² + y² 5y does not exist.

A: To show that limit does not exist.

Q: Can I get help step by step with this problem please?

A: Given:

Q: Use L'H rule to find (a). lim zlng, (b). lim zn ez 1

A:

Q: lim (x,y)→(0,0) x² – y? x2 + xy + y? II

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Q: V1+3x-1 lim Answer: 1 %3D

A:

Q: 10. lim 2-と is A. -1

A: we have to find the value of the given  limit  lim    x→-∞2-x2x

Q: Is it possible to find numbers a, b and c so that an lim n+0o bn3 + cn erists but not equal to 0?…

A: Consider the function:

Q: + 34, find f '(x) using the definition f '(x) = lim h→0

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Q: Evaluate the limit. ΣΗ. 2i + 1 lim i=1 =W

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Q: Use the –δ definition to prove that lim x→1 (3x + 5)/2 = 4.

A:

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: s(2) is continuos if lim f(z) =f(z,)

A:

Q: Determine the values of the following limits. lim 2a? 2x + 4 lim %3D む+1 lim I -1 x -1

A: To find the value of the following limits.

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

A: