lim is x-0 X O A. 0 О в. 1 C. 8.

Q: Show that (2o + h)" – 2ö = nz- | n-1 lim h→0 h for any zo E C.

A: To show: limh→0z0+hn-z0nh=nz0n-1for any z0∈ℂ

Q: 2h 4. lim h0 2h S(x) dr

A: Answer and explanation is given below

Q: - «) lim (2 – ez x→0

A:

Q: e*(1-e*) (1+ x)[ In(1–x)] 12. lim, 0 'x0

A: Recall: If we have 00 form then we apply L'Hospital Rule.i.e, limx→a f(x)g(x)  = limx→a f'(x)g'(x)

Q: 3. EVALUATE AS AN INFINITE SEMES: 0.5 a. e dx lim x- In (1 + x) b.

A: We know that, ex=1+x1!+x22!+x33!+x44!+.........................=∑n=0∞xnn! and…

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: 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: 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: 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: fr'e* for 1 <x<3' for 0<x<1 If (x)= {e then limf(x) is A. O В. 1 С. е D. e E. nonexistent

A: The given function is defined for the interval [0,1) and (1,3].

Q: Find lim eR dt x 00 1/e 1 e

A: We will find first integration then after we apply limit

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

A:

Q: 22 -y2 =? lim (z,1) (0,0) +y? O A. 0 O B. 1 OC. -1 D. Does not exist Reset Selection

A: Explanation of the answer is as follows

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

A:

Q: - 2 lim c. x→o Sin(x)

A: It is given that X approaching 0 from the left, X&lt;0. Therefore, Sin(x)&lt;0. Therefore, the…

Q: e2t - e-2 – 4t lim- t- sint

A:

Q: 3 k3 -ル+} (my)0, t) 4 +n -y lim

A: Given that  Limit

Q: 2 sin? x lim х-0 5x(1+сos x)

A: Let L=limx→ 02sin2x5x1+cosxlimx→ac·fx=c·limx→afxL=25limx→ 0sin2xx1+cosxPlug in the value…

Q: I. Evaluate the following limits. 1 1 1. lim x→1+ x – 1 er – e - -

A:

Q: 4 Find Lim x-0 2e* – 12 А. В. C. - 0.4 D. 0.5 Select one: O A O C O D NIN 13

A:

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

A: See the attachment

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

A:

Q: Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

A: We will use Chebychev's inequality to find the required limit of probability.

Q: [VALUATE THE LIMIT OF THE GIVEN FUNCTIONS: 3 x→1 TT-X² 2

A:

Q: e n Show that for any &> 0 and S, ₁X₁, lim P(S₁-0 ≥ 8) = 0. =

A: We will use Chebychev's inequality to find the required limit of probability.

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

A: This is a problem of multi variable calculus.

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

A:

Q: a" +b" V lim /x AND= Vab tan x fii lim Anao e 2.

A: Given: iv)limx→0ax+bx21x iii)limx→0tanxx13

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

A:

Q: e? – 1 – z lim 2 z-0

A: The given problem is: limz→0ez-1-zz2

Q: x+y lim In ху (xy)-(1,1)

A:

Q: 2. (a) lim T-cos e (b) lim. -70 In R tim (0) メーール

A:

Q: lim, »00(e² + x)!/z =? O a. 0 O b.1 O. Limit does not exist. O d. e O e. 00

A:

Q: -1 sx3 O A) -0 O B) -1 O C) 7 O D) Does not exist

A:

Q: %3D In(1+x) 3.A) lim P-ove tha t マー0

A:

Q: 5. Show that lim –nx² e dx = 0.

A:

Q: Find the limit. 2 )X lim 1+ x4 O A. O О В. 1 O C. 0 O D. 2

A: We have to find

Q: e" (1-e*) (1+x)[In(1– x)] 12. lim, 0

A: Introduction: In mathematics, limits are the factors at which a feature tactics the output for the…

Q: In(x), 5 s x s 16 f(x) A = lim n- o 2 i = 1

A:

Q: ni eoulav sd no 2x + 5 13. lim x→-2+\x + 1八 +x ber

A:

Q: ー4 1. lim もラー2 t+t+ 1 to

A: limt→-2t2-4t2+5t+1 Plug x =-2 in it (-2)2-4(-2)2+5(-2)+1 Simplifying we get 0/5 = 0

Q: 1. Prove using e-d definition. (d) lim (4x + 3) = 7 x→1 x2 – 9 = 6 - (e) lim x→3 x – 3

A: To prove the limit using epsilon-delta definition

Q: (b) lim æ In(x² + y²) (x,y)→(0,0)

A: