Which property of f(x) = x' allows us to conclude that lim x = 8? x+2

Q: Suppose that lim (x,y)→(3,1) f(x,y) = 6. What can you say about the value of f (3,1)? What if f is…

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Q: Evaluate the limit tan x lim x →0 2x

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Q: et +ex -x²-2 Lim- x-0 sin²x-x²

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Q: Find the limit. lim sin(9x) 5x

A: We are solving the first question and for the next question post the question again and also mnetion…

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

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Q: limit

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Q: Find the constant a such that Va ax +4-2 lim

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Q: Evaluate: 1- cos(x) lim 3x2 X+ 0 Express your answer in 4 decimal places.

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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: By using Sandwich Theorem, prove that lim sin x x-0 r

A: We have to prove that limx→0sin xx = 1 using sandwich theorem. Sandwich theorem states that- Suppose…

Q: lim as x-->0  of (x+1-cosx)/x

A: The given limit of the function:

Q: Evaluate the limit.

A: Given limx→0tan4x9x

Q: Express the limit as a derivative.

A: To express: limit limx→-1x3+1x+1 as a derivative. Concept used: Definition of derivative:…

Q: sin(x – 3) lim X→3 + 6x – 27

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Q: Find the value of the limit: 3 tan(4x)– 12x lim

A: From the given problem:   limx→03tan4x-12xx3   This problem can be solved by the series expansion of…

Q: Evalute the lim sin5x/x(x-1) as x approaches 0.

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Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: Find the limit 1-ex lim x+0 10x2 – 18x

A: Here we have to use the concept of limit.

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…

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Q: Find the limits limx→0+x-1/ln x

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Q: Guess the value of lim x 0 (tanx-x)/x3

A: Given :          limx→0tanx-xx3

Q: 2. Use L'Hospitaľ's Rule to find lim (1+ x)*

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Q: sec(x) – sec(a) lim x - a

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: se L'Hopitals's rule to find lim xIn(e* – 1).

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

Q: Find the limit: (а) lim tan 3x x2 sin27x

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Q: 1 lim sinx x2 x→0

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

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

Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

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Q: Find lim 1-CoS 3X Xう。 tan x -1 lim メー X - X->

A: Solution is given below..

Q: Find the limits limx→0(ex + x)1/x

A: Consider the given limit as limx→0ex+xx

Q: Find the value of the limit: lim x→0* sinx+ tan x

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

Q: Evaluate the limit. 5 sin(x) – 5x lim x3

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Q: Find the limit.   Lim x→∞             (1+2x)5/2 ln x

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Q: Which property of f(x) = x' allows us to conclude that lim x- 8?

A: f(x)=x3 is a continuous function. So, it is continuous at x=2 also.

Q: 1. If V5 - 2x² s f(x) s V5- x? for -1sxS1, find lim,-o f(x).

A: Answer and explanation is given below...

Q: Find lim 2x sin using the Squeeze theorem. x-0

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Q: Find the limit limx→0ln(1+4x)sin3x.

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Q: evaluate using Theorem 2 as necessary.

A: We rewrite the given expression as:

Q: is lim (sec x)ot æ 2

A: Apply exponent rule

Q: Evaluate the limit. (Enter your In(x) lim *1 sin(5Tx)

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Q: Find the specified limit. f(x) - x+2, x > -1 lim f(x) ?

A: The given function is            f(x) = x2,  x<-1x+2, x>-1 We have to find the following…

Q: By using Sandwich Theorem, prove that lim sin r X-0 x

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Q: lim x→0 for sin(4x)/3x

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Q: a) By graphing the function f(x)=(cos2x-cosx)/x2 and zooming in toward the point where the…

A: Graph: f(x)=cos(2x)-cos xx2f(x)=cos2x-sin2x-cos xx2

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

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Q: Evaluate the limit: sinh x2 – x2 lim x→0 sinhx − x

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Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

Q: Find the limits limx→∞(1 + 2x)1/(2 ln x)

A: Given, limx→∞1 + 2x12lnx We know that, limx→ac·fx=c·limx→afx⇒12limx→∞1+2x1lnx Now,…

Q: x-3- – 3VA lim x+0* 0" x- Vx

A: We first try to find the limit  by substitution