x + 2| lim X→ -2- X + 2 lim sin X→-5 (동) TC X.

Q: tan 3x lim x→0 \ e2x – 1 3/2 O 1/2 O 2 O 2/3

A: Solution:GivenTo find the limit oflimx→0 tan 3xe2x-1=?Formula:ddxeax=aeaxddx tan ax=asec2 ax

Q: What is lim x=inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^(3n)] + 2? (express answer as x,y)

A: Solve the following

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

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

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Q: Now, use direct substitution. 1 lim X-2 x + 7 + 3) = 1/6 Thus, the value of the limit X + 7 lim X -…

A: limx->21x+7+3Directy substitute 2 for xlimx->212+7+3 13+316

Q: Calculate the limit for the given function and interval. Verify your answer by using geometry.…

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Q: Use the definition of a limit to show that (i) limx→0 (x^2 + 6x + 9) = 9 (ii) limx→−7 and…

A: Authoring guidelines:…

Q: lim 1 + X00

A: Let, L=limx→∞1+1xxlnL=limx→∞ln1+1xx⇒lnL=lim x x→∞ln1+1x

Q: What is the limit of limx→ sin x? 1/2 1 -1 10

A: Given

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: lim Vx +x+1 x- - X-∞

A:

Q: Find the limit. lim sech(x) X -0

A: To find limit: limx→-∞sechx Solution: We know that sechx=2ex+e-x Therefore,…

Q: Determine the value of the limit if it exists. If it does not exist, explain why. ry? lim…

A:

Q: (fif2..f)is di fferentiable at x, proofthat ... by using f(x)– f(*.) f (x)=lim, x-x,

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Q: Evaluate the limit. 1-x² lim *+1 sin(27x) a) lim b) x+2x² C) lim - - 2x *→(π/2)- (2-) tan r Show all…

A:

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

A: limx→0tan(2x)tan(πx)

Q: Please help. I am not sure how to compare the limits when x=0 and y=0. I am not sure what other…

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Q: Calculate the limit for the given function and interval. Verify your answer by using geometry.

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Q: explain why the limits do not exist.  lim (x approaches 0)  x/|x|

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Q: x³-8 4 x+2 x 16 2. lim

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Q: Find the limit of  lim(x,y)→(0,0) (x^2 + y^2)/(sqrt(x^2 + y^2 + 1) − 1 rationalize the denominator

A: To find the limit value :

Q: 5) Does the limit |x+1| lim x-1 x+1 exist? If yes, find its value, if not - explain why. Show all…

A:

Q: Find lim f(x) and determine if continuous at x =2 エ→2

A: We have to check

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…

A:

Q: Find the limit 10xy lim (2,y) → (21, y1 ) 25x2 y2 at the following points. - 10xy lim (a,y) → (0,11)…

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Q: RAGLIO Use a table of values to estimate the value of the limit of lim Vx + 4 – 2 2. f(x) f(x)

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

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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: Explain why f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths in…

A: We have to explain why fx,y must approach a unique L as x,y approachesa,b along all paths in the…

Q: Find the limit. sin(x – 3) lim х>3 x* + 5х — 24

A:

Q: x²y lim (x,y)→(0,0) x2 + y?

A:

Q: Find the limits limx→0(ex + x)1/x

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

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

A: Given: limx→11-x1-x for evaluating given limit, we factorize denominator and find limit

Q: 4. Find the following limits. Remember, show your work. x2 + 2x – 8 a. lim x+2 x2 -x - 2 b. lim sin…

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Q: Find the limits lim x→1- sin-1x

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Q: Let's start by reviewing some limits at infinity. Remember that the techniques we use are a bit…

A: To compute :                   1)   limx→-∞3x4 - 2x25x4 - 7                        2)…

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

A: Left hand limit: Right hand limit:

Q: xy? lim (x,y)→(0,0) x² + 2y4 Compute the limit

A: Given limit,

Q: Figure out that this statement is true or false? if is false explain why?  by using example, and if…

A: Let us take a piecewise function:

Q: Use L'Hospital's Rule to evaluate the given limit. x+x a. lim X--0 sinx b. x-1+ lim -) In x, c. lim…

A: Let us consider a limit function limx→af(x)g(x) If the limit is of the00 form then L'Hospital rule…

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: 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: Use continuity to evaluate the limit. 8 + Vx lim 8 + x

A: We have to evaluate limx→18+x8+x Important formula  If fx is continuous function then limx→afx=fa

Q: Does the limit |r +1| lim 1-1 r+1 exist? If yes, find its value, if not - explain why. Show all the…

A: We need to show that limx→ -1x+1x+1 doesn't exist. So,               limx→ -1+x+1x+1x+1 is positive…

Q: Compute the limit below. Justify your answer. sin(24x) lim- 39x

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Q: Find the limits using any appropriate method. ex-e-x-2x 4.4 #40 lim x-0 x-sinx

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Q: Calculate the limit for the given function and interval. Verify your answer by using geometry.

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Q: Find the limits. Are the functions continuous at thepoint being approached? lim x →π sin (x - sin x)

A: