Let ƒ : (a,b) →R  be an uniformly continuous function. Finish the proof by showing that the limit lim_(x →b)ƒ(x) exists.

Q: limx = 0

A:

Q: Show that the Product Law cannot be used to evaluate the limit

A: To show product rule can not be used to evaluate the limx→π2(x-π2)tanx

Q: 6* - 2* lim,

A:

Q: evaluate the limit using continuity. lim (х,у)-- (2, —1) (xy – 3x²y³)

A: Given: limx,y→2,-1  xy-3x2y3

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: Find the limit. lim tan-! (In)

A:

Q: Evaluate the limit using the Limit Laws: lim (5x - 1) =

A: We have to evaluate the limit using limit laws: limx→25x-1 We know difference law of limits:…

Q: What go in the blank as limit approaches 0:

A:

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

A: limx→afxgx=limx→afxlimx→agx,   limx→agx≠0

Q: Find the limit, if it exists. If the limit does not exist,explain why.

A:

Q: In (x) — х + 1 lim x² 2х + 1 x→1

A:

Q: Use E-S limit definition to prove lim -Im

A: limx→af(x)=L implies that ∀ε>0, ∃δ>0 such that  ∀x≠a, if |x-a|<δ, then |f(x)-L|<ε.

Q: Evaluate the limit. hr lim (1+-

A:

Q: Give an example of a limit of the form ∞ / ∞ as x→ 0.

A:

Q: Find the limit: lim, G-). -i B) does not exist pdf.6 (A) يملع الانتقال إلى السؤال التالي إجراء تغي…

A:

Q: Compute the limits that exist. lim x---2 x/x - 2

A: Explanation: Given that,  limx→2xx-2     Concept Used: If LHL=RHLLim exist.If LHL≠RHLLim doesn't…

Q: Find the limit, If it exists. x- 1 lim X---

A:

Q: assume that lim (х,у) --(2,5) to find the limit. lim 8(x, y) =7 (х.у) -> (2,5) f(x, y) = 3, lim f(x,…

A: Given that, limx, y→2, 5fx, y=3    and   limx, y→2, 5gx, y=7   To find:  limx, y→2, 5fx, y2gx, y…

Q: Find the limit. lim (5x + 4x + 3) X--3

A:

Q: 3. Find the limit. lim (tanx – secx) n-- 2

A: given,       limn→π2-tanx-secx

Q: Evaluate the limit lim sin-(÷).

A:

Q: Prove the limit. Using the precise definition of a limit. lim x approaches 5 (x2-x-6).

A:

Q: Use the definition of limit to show that lim x, = 0. Inn a) Let x,

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: Find the limit, if it exist の十2 lim

A:

Q: Determine the infinite limit. lim - In(x) -0-

A: To find limx→ 0+8x-lnx

Q: Use different path of approach to the point (0, 0) to show that the limit lim(,9)→(0,0) 4 does not…

A:

Q: Find the limit using direct substitution. lim                      3x+1/2-x x-->-2

A: In the direct substitution method, straight way substitute the limiting vailue of x in the given…

Q: Evaluate the limit. lim     ex-x2x  →∞

A: limx→∞ex-x2

Q: Calculate the limit limx→π/2(tanx)cosx.

A: We have to evaluate limx→π2tanxcosx We know that tanπ2 is not defined. Therefore, we will simplify…

Q: Show that the limit lim- X0 X does not exist

A:

Q: Evaluate the limit: lim (1+sinx)

A: Given query is to find the value of the limit.

Q: evaluate the limit using continuity. 2x2 lim (х. у) -> (-2,1) 4х + у

A: Given

Q: Compute the limits that exist. lim x---0, x2 + 3x/x

A: Given: limx→0x2+3xx

Q: Evaluate the limit using the Basic Limit Laws

A: To find the limit  limx→5x-2

Q: lim Z-y)-(0,0) z4+y?

A: To determine the limits of a multivariate function , Convert the limits into one variable and then…

Q: Evaluate the limit or determine that it does not exist.

A: To evaluate the limit lim(x, y) → (3, 4) 1x2 + y2.

Q: What is the Limit of identity function?

A: we have to tell what is the limit of an identity function.

Q: Explain how to convert a limit of the form 0 * ∞ to a limit of theform 0/0 or ∞ / ∞.

A: we have to convert a limit of the form 0 * ∞ to a limit of the form 0/0 or ∞ / ∞

Q: use the epsilon-delta definition of a limit to prove that

A: We have the given limit limx→3x2+1=10. We have to use ε-δ definition to prove the given limit.

Q: By considering different paths, show that the limit doesn’t exist. lim (x,y)→(0,0) xy4/ x2+y8

A: Answer

Q: Prove using the formal definition of a limit that: limx→3 (2x + 2) = 8

A: Given limx→3(2x+2)   = 8Right hand limitlimx→3(2x+2)Let x = 3+h    where h→0hence limh→0(2(3+h)+2) =…

Q: Find the limit, if it exists. lim (---)

A: Given that a limit problem and we solve this problem by using general property of limit.   Here i…

Q: Evaluate the limit, using L'Hopital's Rule if necessary. In x lim

A:

Q: In VT lim x2

A: Solution and Explanation is given below....

Q: . Suppose f(т/3) — 5, f (т/3) — —3,а sin(3та) 2->0 sin(5Tx) . Find the limit: lim

A:

Q: Find the limit. lim sech(x)

A: Given:limx→∞ sechx

Q: Estimate the limit numerically or state that the limit doesn't exist: sec (2) lim (Enter DNE if the…

A: To estimate the limit of the given function at x->1+ . Since the given function is continuous in…

Q: Express the limit as an integral. Š (5(x; )² – 3(x; )³)ax over [0, 2] lim

A:

Q: Evaluate the limit using L'Hospital's rule 9* – 13" - lim

A: From the given problem: limx→09x-13xx Now solve the limit: limx→09x-13xx=90-1300=1-10=00…