e(k-1)a – 1 lim | Bk eit – 1 x→0

Q: 4. Let 1 4- t ift 2 Find the value of c so that lim B (t) exists. t-2

A:

Q: Suppose lim, An = 1. Prove that 1 lim E(-1)*a2k = 0. n-00 n k=1

A: Given that limn→∞an=1. To prove limn→∞1n∑k=1n-1ka2k=0.

Q: What is limf(x) as shown in the graph? AY 1.14+ 0.76 0.38 -4a -3% -1% 2n -0.38 0.76 -1.14+ O -1 O 1…

A: The graph of f(x) is as shown below :

Q: 4x 7 lim 1+ 3. Compute the limit:

A: Limit of the indeterminate form 1∞ can be solved as:

Q: in z2 Q5. Find the value of the limit: lim in z²+1 .- 기 z→e 2

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the limit. /h² + 10h + 11 - /11 lim h→0* h² + 10h + 11 - /11 lim h h→0*

A:

Q: Evaluate I (n +) lim as n → 0 Vn[ (n + 1)

A: We have to evaluate limn+32n⋅n+1 as n→∞ that is limn→∞n+32n⋅n+1 We know that n=n−1! Hence,…

Q: 1. Find the limit. t² 4 8 lim t-2 +3

A:

Q: A. Evaluate the limit in each of the following: 1. lim -1) A-0

A: Limits

Q: (1) Evaluate the limit, if it exists. (a) x² + x - 2 lim t→1 x² - 4.x + 3 (b) x - 81 lim x→81 Vx - 9

A:

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

A:

Q: ΜΑΤΗ-101A 7. Find the limit. lim ( x2 cos x→0

A: We have to solve the given expression   limx→0x2cos1x

Q: 12. Suppose f € C[0, 1]. Prove that lim | f(a" )da = f(0). n>00

A:

Q: 6. Evaluate the limits. sin(0-4) а. lim Ө-0 Ө-4 4w b. im woo 20w+1

A: It is required to calculate the limits of the following expressions:For part (a):

Q: in Q5. Find the value of the limit: lim in — е 2 2+1 Z→e 2

A:

Q: Ql(i) Prove that Lim t* ... /2n²+1 2n²+n]

A: The series is Lim12n2+1+12n2+2+......+12n2+n=12

Q: 1. Evaluate the following limit: x? -4 a. lim- 1+2x + 2x – 8 (x²-9) 2 b. lim 1+3 (x -3) (t - 3) c.…

A: If putting the value of variable value of function approaches 0/0 we should apply L hospital rule…

Q: Find all values of c such that the limit exists.

A: Our Aim is to find the value of c from the given expression such thatthe limit…

Q: Show that for any &> 0 and Sn = 1X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. n-00

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

Q: 4x In z (a) Evaluate lim エ→1( (1- 2)-- -1) C.

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

Q: 19 let ɛ > 0 be arbitrary. Determine & as a function of e 2 In formally proving that lim -x + 8 1/4

A:

Q: II. Apply the limit laws on the following: lim (Vx/VA) 2. X+1 cos x x5+ lim X-3 3. X-1

A:

Q: 5.6. Prove that: (b). lim z0 Z (а). lim does not exist, = 0. - ||

A: The given problem is to prove and evaluate the following complex variable limits.

Q: Evaluate the limit lim[e2"+1– 2e*]. x-0 -1 This limit does not exist. O 1

A: Using formula of limits

Q: x - 4 8. Prove that lim Vr = 2 using the e-6-definition. Hint: Vr - 2 = %3D VI + 2 4

A: The ∈-δ definition of a limit is: The limit of a function f(x) as x tends to "a"  is L, that is,…

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: 1. (a) Use the e - 8 definition of a limit to prove lim(7x + 3) = 38. X5 t010-1123.then fex)-LI…

A: Given,

Q: Find all values of c such that the limit exists.

A: Given: limx→cx2-5x-6x-c for finding value of c for given limit to exists, we factorize numerator of…

Q: 1 Find the limit: lim X-I x+1

A: Our Aim is to find limx→(-1)-1x+1 -(i)

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

A:

Q: 1. Evaluate a) lim b) lim X-T K1O the limit sinx x²-x2 4 In (1-x) + x + == x² 2 23

A:

Q: 9) Find the limit. lim f (z) æ – 2| ( (z) = 2- 2 Graph method

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Let an 2n+4n-3 Using the definition of the limit, prove that lim,∞ an 3n2+2n+1* 2/3.

A: Given that, the rational function  an = 2n2+4n-33n2+2n+1 To prove that limit of function is limn→∞…

Q: Let fn(x) = n²x²(1 – x) on [0, 1]. Does lim,-00 So fn(x) exist?

A:

Q: 22) Find the limit equation of f'C4) if リメト=(×23 で allim Jx -2 x-4 b) lim X-4 C lim x-4 X-L X-4 a)…

A: Here we will find the limit equation for f'(4),

Q: (3+4y-y is th e of lim y+ oy +3y+4)

A:

Q: 2* k! k=1 you would compute 0-0- Ak+1 lim lim ak

A:

Q: e -e lim is z0 In(1+ 2x)

A: Given limit:

Q: lim- -po0(/ + a – 2)=? O a. 00 O b. 1/2 O .0 O d.Limit does not exist O e. 1

A: To find:            limx→∞x2 + x - x

Q: 5x 3 lim 1+ Compute the limit: x→

A: We can have a approach for this kind of question in which we get indeterminate  form 1∞

Q: 3 Evaluate the limit lim [(2-1)(3– 2i)+1–3i] and use the definition of the limit (e-6) z-2+i to…

A:

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

A:

Q: 1. Find lim,→0 k e'

A:

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

A:

Q: 4x 7 lim 1+ Compute the limit: x→0

A: here we put value of limit then we calculate

Q: 7(z +h)- 722 (d) Compute lim h40 h 1 1 I+h (e) Compute lim-

A:

Q: Find the limit. lim x5 In x x-0* O 1 O 5 O-1

A:

Q: 2. find: en(x?) a). Lim メ-1 b). Lim 1 - cos "x 1-COS 4x2

A: