Domain: x* lim f(x) = x3 lim f(x)= x-3- lim f(x) x-3+ lim f(x) = f(0) = f(x) = 0= x3D}

Q: evaluate the limit.

A: Given:

Q: lim x--> negative 0.      f(x) lim x--> 4.      f(x) lim x--> positive 0.      f(x) lim x--> 2.…

A:

Q: The graph of a function f for which f(2) does not exist but lim f(x) x-->2 does exist. create an…

A:

Q: lim (x² + 4x) 2. X→-4

A:

Q: lim tangx X->즐 (쫄-x n2.

A: Given: limx→π2tan2xπ2-x 00 form If limx→afxg(x) is of the form 00, then we use L'Hospital's rule.…

Q: Sketch the graphs of functions that have the given limits and values. lim f(x)= infinity x-->2-, lim…

A: Given limits for the function is limx→2-fx=∞ ,  limx→2+fx=-∞ That is when x approaches 2 from left…

Q: lim x---2, x2 - 4/x - 2

A: We have to find the limit: limx→2x2-4x-2 This is 00 indeterminate form of the limit. Rewriting the…

Q: Оuestion: 2 Use the numerical method to find lim 3-x

A:

Q: Evalugte lim(3x-1)/x Xー>○ X/2

A: The solution is :

Q: limx-> f(x)=3    find limx->1((f(x))2+2)

A:

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

A:

Q: lim X+2 X- 3 X-2

A: "Since you have asked multiple questions. We will solve the first question for you. If you want any…

Q: Create a table of values for the function and use the result to estimate the limit. Use a graphing…

A: Create a table of values for the function as follows: x x4-1x6-1 0.98 0.994-10.996-1=0.67334…

Q: lim 3x/x+1 = 3 x--> infinity, ε = 0.5, find smallest N > 0

A: Answer

Q: Lim x approaches to - infinity (5-1/x)

A:

Q: lim x approaches 2/3 .............. (8 - 3s)(2s - 1)

A: We have to find the limit: limx→238-3s2s-1 This is determinate form of limit so we just have to put…

Q: lim- x-0 X

A: Given :limx→05x

Q: lim x approaches 9 ........ [(x)^1/2 - 3]/(x - 9)

A: limx→9 x-3(x-9)When put x=9, then00 form occur

Q: LValuate limit lim X-> (x²-4 x+! -\x-1\

A:

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

A:

Q: 25 using a table of - 3. Evaluate lim x→25 Va – 5 - functional values.

A: We have to evaluate the given limit: limx→25x-25x-5 Since given limit has 00 indeterminate form so…

Q: 5. Determine the value of a such that lim Va-x - V8+x exists. Then determine the value of the x-1…

A: To determine the value of a such that limx→1a-x-8+xx-1...(1) exists.

Q: 2) lim-(x-) ta tan x

A:

Q: 2 メーズ Lim メ→&-X

A: Evaluate: limx→∞ex-x2ex-x

Q: lim x-0+ \x 1 = lim x2, 1 lim x0+ x2 1 = +0 - (+0) = 0 - - - -- %3D x-0+ x

A: It is infinity minus infinity type of indeterminate form.    To solve it first convert it into 0/0…

Q: 3. Evaluate: lim -) X-0 sinx

A:

Q: lim x approaches 5  ........ x - 5/[ x2 - 25]

A: Limit of the function is value that function seems to approach as x approaches certain value.

Q: lim x approaches 1  .... [(x^-1) - 1]/(x -1)

A: Consider a limit limx→afxgx. The conventional evaluation of the limit sometimes lead to…

Q: Final Value Theorem:- 6, lim xin) lim xCt) ヒ→ lim (1-z) Xcz) (火(00)に

A:

Q: Sketch the graph of a function with the given limits.

A: let f(x) be a function, has the propertieslimx→1f(x)=∞ , limx→3-f(x)=0 , limx→3+f(x)=-∞

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

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

Q: Using l'tHtospitel's Rule Evaluete lim x3

A: We will keep on applying the L'Hopital Rule until we get a finite numerator or denominator and then…

Q: lim (In x)

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

Q: 6. lim f(x) = , lim f(x) = 0, lim f(x) = -∞, %3D X-2- lim f(x) = 0, lim f(x) = 0, f(0) = 0 X→文

A: Proceed as shown

Q: find lim x-> infinity (V 4.x +x + 2x) or show it does not exist. cannot use l'Hospital's rule. must…

A:

Q: 1.) lim 5-x 2.) lim 5-x 3.) lim 5-x

A: Given query is to find indicated limit.

Q: f -3 -2 -1 -2 -3 2.

A:

Q: 1-cosx Evaluate lim-0 xsinx

A:

Q: 2) lim- x) Tanx

A: The given limit is              limx→π2π2-xTanx we know,     Tanx= sinxcosx

Q: Calculating limits Determine the following limits. lim 11x - 11 + x2 and lim 1x - 11 + x2 xS-

A: Given, limx→-∞x-1+x     and    limx→∞x-1+x

Q: f(2) = lim x--> 1-      (1/f(x))= lim x-->1-       (f(1+x))=

A:

Q: cotX Lim メー→。* (いxー1)

A: First take logarithm on both sides of the equation then use L'Hospital's rule…

Q: Lim x---> infonity positive 4x^3+x^3-1÷2x^3+5×-1

A:

Q: lim f(x)=3 x-->5- and lim f(x)=1 x-->5+

A:

Q: lim x→8 f(x) = 4  and limx→8  g(x)=8   , evaluate limx→8  f(x) +g(x)  /7f(x)   Limit =

A: Given,

Q: Evaluate lim x->2 (x^2 - 4x + 4) / tan^2 (x^2 - 4) without using L'Hopital's Rule.

A: