2. 2xy lim (x.y)-(0,0) x² + 2y6

Q: - «) lim (2 – ez x→0

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Q: Suppose that f(x, 0) = 3 for all x ≠ 0 and f(0, y) = 5 for all y ≠ 0. What can you conclude about…

A: The limit of the function, f(x,y) at a point (a,b) does not exist if two paths upon which the…

Q: lim ( + y) In (² + y?) (z.y)-(0,0)

A: We can write the above expression as following :' x2+y2lnx2+y2=(x4+x2y2)lnx2+y2x2. Now, if we put…

Q: Find the limit. y sin x limx.y)(0,1) O 1 8. O No Limit

A: Find the limit. lim (x.y)→(0,1) (y5 sin x)/x To select correct option  1 0 ∞ No Limit

Q: 7. et² -e-y² = }(e - e-1) lim %3D (x, y)→(1,1) x+y

A: To Determine: to prove  lim(x, y)→(1, 1)ex2-e-y2x+y=12(e-e-1) Given: we have a  problem based on…

Q: Find lim (x,y)→(12,3) xy cos(x – 4y). OS 1. –36 2. 36 3. 3 4. 0

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Q: 1S 章テ(メ) H+3x寸hen lim トーつ0

A: the objective is to find the derivative of the given function by using definition of derivative

Q: 2.y lim (x.y)-(0.0) 12x- Show that does not exist. -1ly

A: We will show that limx, y→0, 02xy212x2-11y4 doesn't exist. One path: (along x=0)    limx, y→0,…

Q: -xy lim (x,y)→(0,0) x²+y2

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Q: Find lim "(x.y)→(0,0) (4 + (x² + y? ) In(x² + y² )) Dose not exist O 1 4

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Q: 3* Evaluate (a) lim sin y and (b) lim y x-1 Vx +5

A: we have to evaluate the following: a)  limy→π3 siny b) limx→-13xx+5

Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO FO x-5 • lim х-5 х2-25 = 10 FO

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Q: 1. Show that z³+y³ lim (x, y) (0,0) 1² + y² does not exist.

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Q: Find the Limits: sin (X'ty(0,0)

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Q: 3. Show that lim(r.y)→(0,0) xy =0. (Hint: Use the fact the y| = Vy² and therefore y|< Vx² + y²)

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Q: Find lim. Sin (X/y X-T/4

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Q: 2x + 1 If t(x) find lim,-o t(x) %3D 8x + 1

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Q: -xy س3: أحسب lim (x,y)→(0,0) x²+y² إضافة ملف

A: See the attachment

Q: .2.4 lim (z,y)→(0,0) x² + y?

A: follow next step

Q: の3 Find lim メy <xiy)-s(0,01 x+y² along the curve y=x²

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Q: lim In(x2 + y?) (x,y)-(0,0)

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Q: 2-y lim 7+ 6y² y-

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Q: .2 lim (x, y) (0,0) along y = x2 |3|

A: Substitute y=x2 in the function. Now the limit becomes

Q: X-4y lim (x, y)- (0,0) 6y+7x

A: limx,y→0,0x-4y6y+7x Take the path y=mx, then as x→0, y→0 limx→ox-4mx6mx+7x limx→ox1-4mx6m+7…

Q: 5. Apply L'Hopital's rule to determine the limits of the function. y = lim e"(x – a² + 9)

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Q: Along the path x = e' find y²+6xy lim (x,y)→(1,0) 3x-y-3

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Q: tan X AWO Lim メーラク メ O Lim 2, 5+s° (3) Lim J-→の y生チンチアメチタ

A: Since you have posted multiple question in this question so I have solved first three question…

Q: Txーt e lim 4x² 4,2 +4x

A: Given that limx→0 e2x-14x2+4x We have to find the limit using L-Hopital rule L-Hopital's rule: If…

Q: .2 lim (x,y)→(0,0) x² + y²

A: Consider the given: limx,y→0,0x2x2+y2Let y=mx

Q: Evaluate limx=0+ e(1/x)

A:

Q: (3 + 5y +7{ ) 2+y? 200 + y02 exists if lim r)(0.0)

A: This is a problem of multi variable calculus.

Q: lim 4y° + Jy18 – 1 -00

A: Given that: limy→-∞4y9+y18-1

Q: (b) lim (r + 1) In x

A:

Q: of

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Q: -xy اس3: أحسب lim (x,y)→(0,0) x²+y2

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Q: x+y lim In ху (xy)-(1,1)

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Q: Along the path x = e" %3D find y +4xy lim (x,y)-(1,0) 3x – y - 3 does not exist O -2 -3 2 0 3

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Q: cos x In(x – a) | 40. lim In(e* – e) X→a+ -

A: Use L hospital's rule when of the form type of inderminate 00.

Q: 5. lim (ex – V2x) x→0+

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Q: nx + 1 If lim エ→+0 = 9, find n. 1 %3D nx -

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Q: (4x – 5y) lim (x,y)→(1,1) 5x² – 7y O -1/2 O 1/2 Limit DNE

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Q: 2,,2 x²y² lim (x.y)→(0,0) x4 + 3y4

A:

Q: lim, S(x), given 7-4x. x < 1 S(x) = { %3D x² + 2 x 21

A: Given: fx=7-4x,  x&lt;1x2+2,  x≥1

Q: 2 cosh 2, 2 0. Then the lim f(x)

A: Given function is fx=2coshx , x&lt;0sinhx  , x≥0

Q: Evaluate the limid lim X'sin t X→o sin x?

A: We have to find limit

Q: х — 1 If y = lim x→0 Vx + 3 – 2 The value of y = 4. %|

A: Given:

Q: 2xy lim (x.y)-(0,0) x² + 2y6

A:

Q: Show that (x + 1)² sin y lim (x,y)→(−1,0) (x+1)4 + y² does not exist.

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Q: Find lim (x2 + y?)ln(x² + y?) (x,y)-(0,0)

A: To findlim(x,y)→(0,0)(x2+y2)ln(x2+y2)

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.