(x+h)³ – x³ 14. lim h →0 h

Q: x²-2xy+5y²+1 lim (x,y)→(0,0) 3x²+4y²+2

A:

Q: (х-а) 2. lim Vx-Va X→a

A:

Q: Find the limit (if it exist)

A: Given:

Q: 2. 2xy lim (x.y)-(0,0) x² + 2y6

A:

Q: f" (h+x)-f" tx) Then lim %3D

A:

Q: x + tan x 2? — 5х — 14 - (а) lim x0 3x + 4x² (b) lim (Do not use L’Hospital rule in part(b)) x7- x2…

A: Using rules of limit's.

Q: х2 +x — 2 Vx + 4 – 2 - - (а) lim x→-2 (b) lim x + 2 y y 2 1.00 1 0.75 0.50 -3 -2 - 1 1 2 3 -3 -4 -3…

A: (a)limx→-2x2+x-2x+2blimx→0x+4-2x

Q: x² - 7x y +12y Evaluate lim(x,y)→(3,1) х- Зу

A: The given expression is limx,y→3,1x2-7xy+12y2x-3y

Q: 3 k3 -ル+} (my)0, t) 4 +n -y lim

A: Given that  Limit

Q: lim x-4y (x,y)- (0,0) 6y+7x .A does not exist.

A: To calculate the given limit: limx,y→0,0x−4y6y+7x

Q: x--2xy lim (x,y) - (2,1) x²-4y² .A 3 .B 1 4 .C .D 1 2 ONIM

A:

Q: f(z) = 7. Use f'(x) = lim e+h-©) to find f'(x). %3D %3D 3z-7

A: The given funciton is:fx=23x-7To find f'x

Q: lim Vn² +n –n=0 -

A: Given Lim n-infinity √(n²+n) -n When we pit n is infinity directly we found a infinity-infinity form…

Q: + h 4 (a) Lim×-1'x+1 X (b) Lim h→0 V5h + 4 – 2 -2 - t3 – 1 3. (c) Lim t-1 t-1 II

A: To show the given limits, we use the algebraic indentity and rationalization of a fraction.

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

A: See the attachment

Q: x2 – 4, x 3 -

A:

Q: 54. lim 2 (2-x)' 55. lim y r+1 x-1 56. lim (Vx+ +2x-V-2x

A:

Q: lim (x,y)-(-3,4) (x³ +3x²y² - 5y³ +1)

A: Here we have given an expression with limit and we have to solve it. We have lim (x,y)→(-3,4) (x3 +…

Q: 6 lim | 3 x² – 32 X+3 X - Enter I for oo, -I for -00, and DNE if the limit does not exist. Limit =

A: We shall find left hand limit first if it doesn't exist then limit not exist, if exist and finite…

Q: 2-y lim 7+ 6y² y-

A:

Q: lim zx+xて Xー→3 メ-3

A: Apply L hospital rule

Q: 3. Given the function y = [(x² +2x+ 1]/(x), (x0), find: (a) the limit of y as x approaches positive…

A: Given:  The function y=x2+2x+1x, x≠0 To Find:  a The limit of y as x approaches positive infinity.b…

Q: Q2) A) 1-VI+1 sinax 3) lim I+1 1) lim 2) lim

A: Given that:                       (1)limx→∞x+1x2+3 (2)limx→01-x+1x(3)limx→0sin3xx   NOTE: As per our…

Q: find

A:

Q: 2. メー gu)= - fex) = X üls Is1 3メ-1 احب lim (fog) x メー

A: We have to find limit

Q: .2 lim (x,y)→(0,0) x² + y²

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

Q: your a ;) lim x4+メーLo メ→。 i) lim 左十 \im tメーLo X→-∞ iii) \m 4a(a+)しメー2)しメ+ム) メ→ ○

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

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

A:

Q: *+xVア-2) lim )(4,16) x - Vy

A: Here we have lim(x,y)→(4,16)x2+xy-2yx-y

Q: 1 d) limy-→0- e) lim,o (1+ r/n)" 1 f) lim→0 x +

A: L'Hospital Rule : If limx→af(x)g(x) is in the form 00 or ∞∞, then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: tan³ 2x r3 lim x→0

A: Given that: limx→0tan32xx3

Q: 8 lim is x0o 1+81/x А. 8 B. no limit C. D. 4 Е. О o| 8

A: Find limit of a function 8/1+81/x when x tends to infinity.

Q: Q.2 Show that r(ax) _ 1 lim x0 (x)

A: to show  limx→0ΓaxΓx=1a   ...i as we know Γn=Γn+1n using this formula we get Γx=Γx+1xΓax=Γax+1ax

Q: - Find lim Re(2) [Hint: use z = x + iy.] z -1- i - Find lim 2+1+i 22 – 2z + 2

A:

Q: lim (2,y)+(0,0) In(2 + x² + y?) x2 + y?

A: We have to solve given limit:

Q: {x² +7, 14, x = 4 lim f(x), where f(x) =

A:

Q: lim f(x), where f(x) X-2 S11 2x if x < 2 if x 2 2

A:

Q: Jx-2 %3D F(x) x²+x-6 Does lim F(x) exist? x-2

A:

Q: 19. lim x→2- x² – 4 eas y + 6 21. lim y→6+ y2 – 36 -

A: Given that limx→2- xx2-4 limx→6+y+6y2-36

Q: 3x +x 6. Evaluate the limit: lim- x→0 а. О С. 1 b. 3 d. -1

A: “Since you have asked multiple questions, we will solve ONE question for you. If you want any…

Q: x² yey lim(x,y)→(0,0) x4 + x + y²

A: To evaluate the following limit.limx, y→0, 0 x2yeyx4+x+y4

Q: V4 - x2 0sx<2 lim f(x), where f(x) = < 2 9) x-4" 2 sx<4 x = 4 B) Does not exist A) 4 C) 2 D) 0

A: f(x)=4-x20≤x&lt;222≤x&lt;44x=4

Q: x2 – 1 t(2) = 1 What is lim t(x)?

A:

Q: 3+2r lim エ→0 =?

A: Given , limx→03x2+2xx

Q: x²+x5-2y lim (xy)-(3,9) %3D x-

A: Given limit lim(x,y)→(3,9)x2+xy-2yx-y

Q: x2-2xy lim (x,y) - (2,1) x²-4y2 .A .B 1 .C 1 .D 1 4

A: We have to evaluate the following limit. lim(x,y)→(2,1)x2-2xyx2-4y2