Once you know lim x-->a+ f(x)  and lim x-->a-  ƒ(x) at an interior point of the domain of ƒ, do you then know limx-->a ƒ(x)? Give reasons for your answer

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: Suppose that ƒ is an even function of x. Does knowing that lim x-->2- ƒ(x) = 7 tell you anything…

A:

Q: Prove, using the formal definition, that limx→1 (sqrt(1-x))=0

A:

Q: Find the value of -1 tan (5x) lim- X

A:

Q: limx--->0+(1/x8-1/x4). Use l'Hôpital's Rule if appropriate.

A:

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

A:

Q: Evaluate the limit. +4-2 limx→0

A: First rationalize the numerator.

Q: Evaluate lim x->-1 if f(x) {  1/x if x < -1                          { x2 - 2 if x ≥ -1

A: To evaluate: The limit limx→-1fx. Given: The function is fx=1x,        If x&lt;-1x2-2    If x≥-1.…

Q: Evaluate the limit. limx→(π/2)− (x − π/2)tan x Just letting you know the negative sign is…

A: the given limit,limx→π2-x-π2 tanx

Q: Let ƒ(x) = (x2 - 1)/(| x| - 1). a. Make tables of the values of ƒ at values of x that approach c =…

A: a) When x is near -1 then x is negative.  For negative x, we have |x|=-x Using this we simplify the…

Q: Determine the Limit:  Limx-&gt;infinity (1/8)x

A: Consider the given problem:

Q: according to the squeeze theorem, for values of x near a if g(x)≤f(x)≤h(x) and limx→ah(x) = L then…

A:

Q: True or False: We can calculate a limit of the form lim f(x) x-->c simply by finding f(c).

A: In general,  this is false statement.    Answer : False     Reason is below:

Q: limx--->2^-     f(x), where f(x)=2x-5 if x <2…

A: limx-&gt;a- f(x) = limh-&gt;0 f(a-h)

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&lt;x

Q: Find the limits limx→ -∞tan-1 x

A:

Q: Suppose neither limx→0 f(x) nor limx→0 g(x) exists. Show that limx→0 [f(x)g(x)] may exist.

A:

Q: Numerically estimate accurate to 2 decimal places of lim x -> 0 ((2^x -1)/(x))

A:

Q: Estimate the value of limx→2 x 2 + x − 6 x 3 − 8 to 3 decimal places by making a table with the…

A:

Q: Give an example of a function that is not continuous at x = 2 but limx→2 f(x) = 1

A: choose any equation of line such that f(2)=1 but the function function f(x) should be discontinued…

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: Find (a) limxS400+ :x; and (b) limxS400- :x;; then use limit definitions to verify your findings.…

A: (a) Given: limx→400+x  ……1

Q: evaluate  lim -> -2+ ((x+2) cot (x^2+5x+6) do not use lhopitals rule

A:

Q: (a) Estimate the value of                 ___________limx-&gt;-∞(√ x2 + x + 1  + x)   by graphing…

A: Given f(x)=x2+x+1+x

Q: How close to 0 we need to take x so that lnx0 but f(0) does not exist

A:

Q: lim (In x)

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

Q: Find lim_f(x), if it exists. If it does not exist, explain why. X--4"

A: Follow the procedure given below.

Q: lim (In(x))* ?

A:

Q: Evaluate lim-[(sinx-x)/x³] by u

A:

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

A: Given information.

Q: X -1 lim х - 1 X-1 X,

A: We have to compute the limit  limx→1 x-1x-1.

Q: Find the limit  lim x-->infinity:  1/2x + sinx

A:

Q: F(x)={tan(x+3) x3-) f(x) Photo better depicts problem, thank you!

A: Given,           Fx=tanx+3x&lt;-3x+33+1-3≤x

Q: If limx→0+ ƒ(x) = A and limx→0- ƒ(x) = B,find limx→0+ ƒ(x2 - x4)

A: Given: limx→0+fx=A, limx→0-fx=B we know that when x=0+, f0+2&gt;f0+4 so, given limit will be…

Q: Suppose that ƒ is an odd function of x. Does knowing that lim x--&gt;0+ ƒ(x) = 3 tell you anything…

A:

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

A: It is given that limx→4fx=0 and limx→4gx=-3.

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

A: limx→0-xx

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: If f and g are two functions such that lim f(x) as x --> a = + infinity and lim g(x) as x --> a = +…

A: Given: f &amp; g are two functions such that, To check if this statement is True or False

Q: 4 ) lim- (x-.tanx 17

A: Use simple result of limit

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

A:

Q: lim x in (It -)

A:

Q: 1) If lim f(x) = , what asymptotic behavior will be illustrated in the graph of f (x)?

A: 1) If limx→6-fx=∞, then the value of the function fx tends to infinity as x→6 from the left hand…

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: Evaluate: lim --> 0 (x-tanx)/xsin2x

A:

Q: True or false: For lim f(x) x--> c to be defined, the function f must be defined at x=c

A: Solution The objective is determine whether the given statement is true or false

Q: Prove that limx→4 √ x = 2 using the ε-δ-definition

A:

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.