What exactly do limxSq ƒ(x) = L and limxS -q ƒ(x) = L mean? Give examples.

Q: is it true that ∇f(limx)=lim∇f(x) and further that ∇2f(limx)=lim∇2f(x)?

A: We know,  ∇f(xi)=f(xi)-f(xi-h), h=xi-x0i,i=0,1,2...And…

Q: Using L'Hospitals Rule, what is limx->infinity (1+3/x)x

A: Let y= (1+3/x)^xApply ln on both sides.

Q: Suppose limx →4 ƒ(x) = 0 and limx →4 g(x) = -3. Find lim x →4 g(x)/ƒ(x) - 1

A: We first distribute the limit

Q: thelimit, if it exists. \lim _{x \rightarrow-\infty} \frac{x}{\sqrt{x^{2}+1}}

A: Given, limx→∞xx2+1

Q: Use a table of values to estimate the value of thelimit. If you have a graphing device, use it to…

A: Then we make two tables for values on both sides of x=0 From the tables we see that:

Q: Does lim—>1 exist? Does lim—3 exist? Are they continuous? Discontinuous?

A:

Q: If limx→c ( ƒ(x) + g(x)) = 3 and limx→c ( ƒ(x) - g(x)) = -1, find limx→c ƒ(x)g(x).

A: Given limx→C fx+gx=3          limx→Cfx-gx=-1       To find limx→C fxgx

Q: Evaluate the limit. +4-2 limx→0

A: First rationalize the numerator.

Q: Build a table to estimate lim X-0 X

A: Given data:     The given limit of the function is: .   The expression for the given limit of the…

Q: show that : Limx→0    1/ (x – 1) + 1/( x + 1)  ) /x = −2

A: apply the concept of limit to prove the given problem.

Q: If limxSc (ƒ(x) + g(x)) = 3 and limxSc (ƒ(x) - g(x)) = -1, find limxSc ƒ(x)g(x).

A: Given, limx→cf(x)+g(x)=3limx→cf(x)-g(x)=-1   Find: limx→cf(x)g(x)

Q: What is lim In x? x→2

A:

Q: Use a table of values to estimate the value of thelimit. If you have a graphing device, use it to…

A:

Q: The value of lim (xe- x) will be ...

A: It is given that limx→∞xe-1-x.

Q: What is lim ? X-0+ x

A:

Q: What are limx→+-∞ k (k a constant) and limx→+-∞ (1/x)? How doyou extend these results to other…

A: limx→af(x)=L means f(x) becomes arbitrarily close to L as long as x is sufficiently close to a.  We…

Q: Find the one-sided limit

A: Given that limx→π+ xcsc x. Compute the limit as follows.

Q: If limx→0+ ƒ(x) = A and limx→0- ƒ(x) = B,find limx→0+ ƒ(x3 - x)

A: Given: limx→0+fx=A,limx→0-fx=B we have to find limx→0+fx3-x we know that if x∈0,1 then x3<x

Q: Find lim [x csc(x)] as x approaches zero.

A:

Q: Find limx→−∞(x2 −1)e4x. Show work.

A: We need to find : limx→-∞(x2-1)e4x

Q: Find the limits limx→∞sec-1 x

A: In x=sec(y) , as y approaches π/2 from the left then x approaches ∞ So, in y=sec-1(x) as x…

Q: Using L'Hospitals Rule, what is limx->0+ (xsqrt(x))

A: We need to find the value of the limit using L’Hospital’s rule,

Q: Find lim,x - Vx²+ 2

A: To find the limit

Q: Suppose that ƒ is an odd function of x. Does knowing that limx →0+ ƒ(x) = 3 tell you anything about…

A: Given that f(x) is an odd function.  So, f(-x)= -f(x) Given that lim x →0+ ƒ(x) = 3

Q: Once you know lim x-->a+ f(x)  and lim x-->a-  ƒ(x) at an interior point of the domain of ƒ,…

A: If we know the right and left-hand limit of a point then we know the limit at that point.

Q: Show that

A: Here we have to show that;  limx→-∞1x

Q: Evaluate limx-->0 (x^2)/(sin^2(7x)) Without using L'Hospital's rule.

A: A property:L'Hospital's Rule is not necessary here.The following is an important property used in…

Q: Give examples of functions f(x) and g(x) with limx→∞ f(x) = ∞ and limx→∞ g(x) = 0

A: We want to find two functions f(x) and g(x).

Q: If limxS1 ƒ(x) = 5, must ƒ be defined at x = 1? If it is, must ƒ(1) = 5? Can we conclude anything…

A: The limit of a function is very significant in differential calculus. When the independent variable…

Q: Let limx3 f(x)=1 and limx3 g(x)=2. Find limx3 x2(f(x)+2x)/f(x)g(x)+3

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Using L'Hospitals Rule, what is limx->infinity (ex + x)(9/x)

A: Given information.

Q: Evaluate exactly lim (1 + sinx)²cotx x→0

A: This question is indeterminate form of 1infinity and solved using L Hospital rule.

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Given: limx→0 xx=1 To determine: Given statement is true or false.

Q: Suppose that ƒ is an even function of x. Does knowing that limx →2- ƒ(x) = 7 tell you anything about…

A: Even functions are symmetric about the y-axis for example: if we know f(1.99) then f(-1.99)=f(1.99)…

Q: Find limx approaching infinity (x+2/x-1)^x

A:

Q: Suppose limx →c ƒ(x) = 5 and limx →c g(x) = -2. Find lim x →c ƒ(x)g(x)

A:

Q: Given the function f(x) = sqrt(x-2), please evaluate the limit. limx→∞ f(x)

A:

Q: What exactly do lim, »∞ f(x) = L and lim,_-∞ (x) = L mean? Give examples.

A:

Q: Find the value of lim tanx

A: As per our guidelines we only solve question number 1 . If you want the solution of other parts…

Q: find the limit limx -> 3 of [root(x+6) -x] / (x^3 - 3x^2)

A: To determine the limit of given function.

Q: please kindly evaluate the limits and or explain why it does not exits  Limx->1 (1/x2+1)

A:

Q: Determine limx→−2 6/x-2, if it exists

A: limx→−2 6/x-2 yes limit exist and we can direct apply the limit so put -2 in given function…

Q: can you please write this part in handwriting? the characters are in different format so im having a…

A: Solution

Q: use f(x) to find: limx→0f(x), limx→-4f(x), limx→5+f(x), limx→-4-f(x). the discontinuity that is…

A:

Q: If you know that limx →c ƒ(x) exists at an interior point of a domain interval of ƒ, can you find…

A:

Q: By using Sandwich Theorem, prove that lim sin x

A:

Q: Find the limits limx→∞csc-1 x

A: Given:limx→∞ csc-1x

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.