Find the value of the postive constant c, such that  lim x->infinty ((x-c)/(x+c))^x=1/4

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

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: find limit ,if exists \lim _{x \rightarrow \infty} \frac{8}{4-10^{-x / 2}}

A: To find: The limit of . Calculation: The limit of can be obtained as,

Q: Create a table of value (use 8 values- 4 on the left and 4 on the right) and a calculator to the…

A: topic- limits

Q: Clearly show why evaluating lim x (In x)2 requires repeated application of L'Hopital's rule. Show…

A: We have to evaluate the limit of the function fx=xlnx2 using the L' Hopital's rule. To find the…

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

A:

Q: \lim_(x->-\infty )((13x-2)/(x^(3)+14x-4))

A: Divide the numerator and the denominator by x3.…

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

A:

Q: Find the limit if it exists: lim x->0       (sin(3x)) / (x(3x2 - 5))

A:

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: find the limit.  lim(x-->2^-)    ln(-1/x-2)

A: Here we have to find the left hand limit at x = 2.

Q: Investigate:

A:

Q: Use a table of values to estimate the value of the limit (correct to three decimal places). If you…

A: In the given question, we have to estimate the limit of the function by using the table and graph.…

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 or show that it does not exist. \lim_(x->\infty )((sin^(2)x))/(x^(2)+1)

A:

Q: 4) lim -。 ,(-1<x<り nや0

A:

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

A:

Q: Find the limit. (Hint: Treat the expression as a fraction whose denominator is 1, and rationalize…

A: To compute the limit by rationalizing the given function

Q: Find the limit. lim x--> 0  sin x/2x-sin x

A:

Q: lim f(x) x--&gt; 3, where f(x) = {2(x+1), if x &lt; 3 or 4, if x = 3, or x^2 - 1, if x &gt; 3}…

A: First we find the limit of f(x) from left side and right side .

Q: 2 メーズ Lim メ→&-X

A: Evaluate: limx→∞ex-x2ex-x

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

A:

Q: B] Using L'Hopital's rule, Find lim y.In

A: Given: limy→∞y.lny+1y-1 Apply L Hopital's Rule. limy→∞y.lny+1y-1=limy→∞y.lnddyy+1ddyy-1

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

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

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

A: The limit of a function at a variable is equal to the value of the function when the value of the…

Q: If you know that lim x--&gt;c ƒ(x) exists, can you find its value by calculating lim x--&gt;c+ ƒ(x)?…

A: If at x=c the limit of f(x) exists then the one-sided limits at that point are equal. So, if exists.…

Q: Evaluate, Lim x-->-2+  ((x+2) cot (x2+5x+6))

A:

Q: If lim f(x) =5 x-->1- and lim f(x)=5 x-->1+, what can you say about lim f(x) x-->1? What can you say…

A:

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

A: Given information.

Q: Find the limit lim x---> infinity sqrt(x^2-1)/2x-1

A: Given function is limx→∞x2-12x-1

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: Find limx approaching infinity (x+2/x-1)^x

A:

Q: Create a table of value (use 8 values - 4 on the left and 4 on the right) and a calculator to the…

A: Given problem:- Evaluate limx→610-x-4x+6by using 8 values table 4 left and 4 right

Q: find the limit of lim x->3 sin(x-3)/x^2-x-6

A: To find limx→3sinx-3x2-x-6

Q: Find the limit.  lim x--> infinity  ln (3x2-1/x2+1)

A:

Q: 2) lim- x) Tanx

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

Q: Find the limit. x-x lim x→11- Vx х-х* lim x→11- Vx (Type an integer or a simplified fraction.)

A:

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: Find the limit. (Hint: Treat the expression as a fraction whose denominator is 1, and rationalize…

A:

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

A:

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

A:

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

A:

Q: Prove lim x ---> 3    (1/3x+1) =2

A: It is known that if we have a function f(x), and limit x tends to a, then the function can be…

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.