If f and g are two functions such that lim f(x) as x --> a = + infinity and lim g(x) as x --> a = + infinity then lim [ f(x) - g(x) ] as x --> a is always equal to 0. Select one: True False

Q: the limits if it exists, if it does not explain why. (1) lim ()" (ii) lim

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Q: Find the one-sided limit (if it exists).

A: Given: The one - sided limit is limx→-1- x+1x4 -1 .

Q: 2. Construct a table of values to investigate 1 if x -1

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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: Suppose lim, =1. Prove that lim -(-1)* = %3D

A: Given: limn→∞ an=1To prove: limn→∞ 1n ∑k=1n -1k a2k=0

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

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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: given that  lim f(x)=9           lim g(x)=-2             lim f(x)=0 x---&gt;1.…

A: Note: We shall only answer up to first three sub-parts as the exact one is not specified. Please…

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

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Q: find the limit or explain why it does not exist.

A: To find the limit  limx→π sec x = ?

Q: use definition of limit to show:   lim    (4x + 1) =13 x-&gt;3

A: The definition of limit:

Q: The value of the limit x42x-3 lim メー)イ X-イ

A: Given : limx→1x2+2x-3x-1

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--&gt;a+ f(x)  and lim x--&gt;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: Evaluate the limit sin 3x lim 5x

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Q: Suppose that ƒ(x) and g(x) are polynomials in x and that lim

A: We have given fx and gx are polynomials in x and limx→∞fxgx=2.

Q: Find the one-sided limit (if it exists).

A: Given limit: limx→12-xsecx

Q: Sketch the graph of the function and use it to determine the values of a for which limx--a f (x)…

A: We will find out the required values.

Q: Find the one-sided limit (if it exists).

A: Given: limx→0+x-1x+3 for evaluating given limit, we put x=0+ in given limit

Q: suppose f(X)->  -250 and g(x)->0 with g(x)>0 as x->2. Determine lim->2  f(x)/g(x)

A: Given: limx→2f(x)=-250 and limx→2g(x)=0 and g(x)&gt;0

Q: Evaluate the limit sin 3x lim 9x

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Q: Investigate the one-sided limits graphically:

A: We have to investigate the one-sided limit graphically of the following function -  limx→0+ ln x

Q: If Lim [x3 – g(x)] = 12 as x tends to 3, use the Rules of Limits to find Lim g(x) as x tends to 3.…

A: Given: limx→3x3-gx=12

Q: Calculate the limit if it exists: lim x→4 for 5/(x-4)2

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

A: Follow the procedure given below.

Q: Find the one-sided limit (if it exists).

A: Given :                       f(x) = limx→2- 1x2-43

Q: Evaluate the limit numerically. x + 4 lim x--5- x + 5

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Q: 3) lim (x² + 1) X--1

A: Limit is a basic concept of calculus  which shows the behaviour of a function  when it tends to that…

Q: Find the one-sided limit (if it exists).

A: To find the limit limx→0-1+1x. We know that 10-=-∞. Evaluating the given limit,…

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

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

A: limx→0-xx

Q: Find the one-sided limit (if it exists).

A:

Q: Prove that lim -- (x + 1)

A: we have to prove that: limx→-1-5x+13=-∞   L.H.S:…

Q: estimate the limit numerically to two decimal places or state that the limit does not exist

A: The value of the limit is 2. Take the first term as common term and simplify.

Q: Show that lim- e +1 does not exist. 1/x

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Q: Calculate the limit.

A: limx→∞tan-11+x1-x

Q: Evaluate the limit  Limx-&gt;0 (ex-1-x)/x3

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Q: Suppose that limx→2[f(x)+x2]=α. Find  limx→1(x+1)f(2x)

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Q: If lim f(x) = - infinity x-->-1+ and lim f(x)=-infinity x-->-1-, what can you say about lim f(x)…

A: answer

Q: 3- If lim f(x) = 3.5 and lim,2+ f(x) = 6.5 , the function has a double sided x-2- limit or one sided…

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Q: —ах+6 if x2-1 Let f(x)=< For what value of a does 2x2 +ах ifx<-1 lim f(x) exist? x--1

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Q: If there is no single value that is approached by f(x) as x approaches a, then lim f(x) does not X→a…

A: If there is no single Value that is approached by f(x) as x approaches a,then limit of f(x) as x…

Q: Suppose that f (x) is a function such that lim f(r) and lim f (r) both exist. Does this mean lim…

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Q: Find the limits limx→0+x tan (π/2 - x)

A: Given that, f(x)=x tan (π/2 - x) We have to find, limx→0+xtanπ2-x

Q: Find the one-sided limit (if it exists) lim 9x tan TX x-(1/2)*

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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: 2) If 2 – x2 < f (x) < 2+ 3x² whenever -1 < x < 1, use limit theorems to find lim0 f (x). Give all…

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Q: Show that a function cannot have two different limits at the same point. That is, if limx--&gt;c…

A: Let f(x) be a function which is defined everywhere in an interval except x=a, then , If for all ,…

Q: Suppose lim f(x) = - 7 and that for all x + 8, x →8 (플+7 + f(æ)) cos 2 f(x) + - 7. Find lim - 7 -…

A: Formula used   *    cos (π2+θ)=-sinθ*      limx→0sin θθ=1

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.