la) Use numerical and graphical evidence to guess the value of the limit x- 1 lim * -Ix-1 Xー How close to 1 does x have to be to ensure that the function in part (a) is within a distance 0.5 of its limit?

Q: Evaluate the limit (if possible) using L'Hopital's Rule if necessary et? - 1 lim x→0 2x2

A:

Q: lim (4.x – 3) = 9

A: The given limit,      limx→34x-3=9

Q: use the definition of limits atinfinity to prove the limit. {lim x approaches to infinity  ( 2/…

A: The function is . The limiting value of the function is to be found out as tends to infinity. To…

Q: Use l'Hospital's Rule to find the exact value of the limit. lim (1 + 8)*

A:

Q: Use the definition of the limit of a function of two variables to verify the limit.

A:

Q: Use l'Hospital's Rule to find the exact value of the limit. (1 + 2)* lim

A:

Q: Let n be a positive integer. For which n are the two infinite one- sided limits lim 1/x" equal?

A: Let n be a positive integer. for which n are the two infinite one sided limits limx→0±1xn equal. for…

Q: 2. Explain why f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths…

A: A number L is said to be the limit of a function f(x,y) as (x,y)→a,b , if for any real number ∈>0…

Q: 34. Show that the Product Law cannot be used to evaluate the limit lim (x - ) tan x. xx/2

A:

Q: 1. Is the limit lim in indeterminant form? Explain.

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Find the limit L. Then use the - definition to prove that the limit is L

A: Given Data The limit is lim x→4 √x.   Evaluate the given value of limit lim x→4 √x, Hence value of…

Q: b. lim -) x-1 Inx

A: The L'Hospital's Rule states that: limx→af(x)m(x)=limx→af'(x)m'(x)

Q: 3. Use the precise definition of a limit to prove lim(9 – x) = 5

A:

Q: 3 – 'ind the limit lim - Vr + 7 x→2 x – 2

A:

Q: use l’Hôpital’s Rule to evaluate the limit

A:

Q: 16) Evaluate the limit (if possible) using L'Hopital's Rule if necessary lim x0 2.x2

A: The given limit, limx→0ex2-12x2

Q: A- Find the limit for th 1. lim tanzx

A: (A)1. limx→0tan 2xsin 4x=limx→0sin 2xsin 4xcos 2x=limx→0sin 2x2xsin 4x4xcos 2x×12=limx→0sin…

Q: 3 lim х-1 \x — 1 х2 + х — 2)

A:

Q: lim -1 x→0+

A: Separate the limit.

Q: lim(4x – 3) = 9 x→3

A:

Q: Find the limit as x -> (+) or (-) oo (Infinity) using L'Hoptials Rule for: Lim as x->oo of (9x +4)…

A:

Q: Determine the infinite limit. X 1 lim x4+ X - 4 -CO

A: We will plug x=4^+ in the expression first. We got 0 in denominator. So lets check by plugging…

Q: Find the limit L. Then use the - definition to prove that the limit is L

A: Given that: The limit is  limx→-2 ( 4x + 5 )           .

Q: 2. If it exists, find lim f(x) where X--1 x =-1 f(x) = { *x– 1)³, x+-1 4, If the limit does not…

A:

Q: What must be multiplied to both numerator and denomination of lim→2 3-г-1 SO 2-x that the limit will…

A: We have to find multiplication factor for given Limit.

Q: Find the limit L. Then use the - definition to prove that the limit is L.

A: Consider the following limit: L=limx→21-x2=1-22=1-4=-3

Q: compute the limit (or state that it does not exist) assuming that lim n→∞ an = 2

A: Answer :  Limit does not exist. Explanation : Here I am attaching the screenshots of the solution

Q: When trying to explain an infinite limit. What does it mean to say that: lim as x approaches 0…

A:

Q: Evaluate the limit. tan x | (Type an exact answer.) lim 7 2х - я

A:

Q: Use l’Hôpital’s rule to find the limits

A: we have to find the limit of the given function limx→π2-x-π2secx

Q: cot(x) – 1 lim 4

A:

Q: Determine the infinite limit. lim 3 sec(x) x- (T/2)+ X 00 - 00

A: Given limx→π2+3xsecx, to find the limit

Q: (a) lim (3x + 5) = 2, I-1

A: a limx→-13x+5=2using ∈-S definitionWe need to prove that :Given any ∈, we can find S , so that…

Q: Determine the infinite limit. lim x cot (x) O 00 O -∞

A: Limit.

Q: Use l'Hospital's Rule to find the exact value of the limit. 9 \X ( 1 + 2)* lim

A: To determine the value of the limit.

Q: 1b. Use L'Hopital's Rule to find the Limit:    lim      2tanx/sec2x x->pi/2

A: To find the limit

Q: One student uses L'Hopital's Rule to find the limit as follows: lim lim 2e lim 2e2 How do you…

A:

Q: Use l’Hôpital’s rule to find the limits

A: We have to find the limits using L' Hospital's rule: limx→-5x2-25x+5 Since it is 00 form so we can…

Q: Evaluate the limit, using L'Hôpital's Rule if necessary. lim X→ 0 In(et-1) dt

A:

Q: Use l’Hôpital’s rule to find the limits

A: The expression limx→03x-12x-1. We have to find the limit of this given expression by using…

Q: 1c. Use L'Hopital's Rule to find the Limit: lim          (1 - x)tan(pix/2) x->1-

A: We will use tan z = 1/cot z formula

Q: Use L'Hospital's Rule to evaluate the given limit. x+x a. lim X--0 sinx b. x-1+ lim -) In x, c. lim…

A: Let us consider a limit function limx→af(x)g(x) If the limit is of the00 form then L'Hospital rule…

Q: Estimate the limit numerically or state that the limit does not exist. If infinite, state whether…

A: Then we make two tables of values as x approaches 0. One for values on the left side of x=0 Other…

Q: Use l’Hôpital’s Rule to find the limits

A: We have to find the limit using L' Hospital's rule: limx→1xa-1xb-1 Since it is 00 indeterminate form…

Q: Find the limit. Use l'Hospital's Rule where appropriate. lim (2x - In(x))

A:

Q: lim x-1 Inx

A: To evaluatelimx→1+(xx-1-xlnx) using L'hospital Rule.

Q: Find the limit. lim (2 – x)6 tan(5) |

A: Explanation of the answer is as follows

Q: Use l’Hôpital’s rule to find the limits

A: Let the given limit be L - L = limx→0 x2lnsecxUsing L-hospital rule, differentiating numerator and…

Q: 5) Find the indicated limit if it exist. а) lim X-2 3- Vx+ 7 2 - x x' +1 b) lim x-- x+1

A:

Q: 1. Use the limit laws to evaluate lim (2x-1)Vx+3 In each step, indicate the limit law applied.

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…