1. Discuss the continuity of f(x) with graph shown below by answering the following questions.

Q: Prove the limit statements lim x sin = 0 y=x sin 2

A: Prove the limit statements     limx→0x sin1x=0

Q: Formally prove that lim 2x+3=7 using the ɛ,8 definition of a limit. x→2

A:

Q: Consider the function g(x) = cos(1/x). We will investigate the limit behavior at x = 0. c) If n is…

A: Given function,

Q: Prove 4x+3 is continuous at x= 4 in 3 different ways:              a. Using the delta-epsilon…

A: According to the given information, it is required to prove that 4x+3 is continuous at x=4 in three…

Q: 1. Express the limit as a definite integral of a function on certain interval and compute the…

A: using the particular form  1n∑r=1r=nfrn=∫01fxdx   and to find the  the derivatiove of function under…

Q: use the definition of limits atinfinity to prove the limit. {lim x approaches to infinity  ( 2/…

A: The function is . The limiting value of the function is to be found out as tends to infinity. To…

Q: 4. Evaluate lim [In(2+x)-In(1+2.x)] using Calculus 1 limit techniques. Show all steps to justify…

A: To evaluate: limx→∞ln2+x-ln1+2x Solution: We know that, lna-lnb=lnab Therefore,…

Q: lim(8x + 16) = 24 Use the epsilon-delta definition of limit to prove that æ→1

A: Let's find.

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: . What is the limit of f (x) = 4 as x approaches ??

A: Let's find.

Q: Consider the limit lim (x-1)sin) X-1 X-1 (a) Can this limit be evaluated using substitution? Why or…

A: To evaluate lim(x tends to 1) (x-1) sin[π/(x-1)]

Q: If f is differentiable on an open interval containing 0 with lim f(x) f(z) = 0 and lim f'() = 2,…

A:

Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim 2 x→1 x´ + x -2

A:

Q: Evaluate the limit of f(x) = - at x=0. (Think about how a limit breaks down to sided limits. What…

A: Given limit limx→01x

Q: Find the limit L. Then use the ε-δ definition to prove that the limit is L.

A: Given that limx→2 1-x2. Obtain the limit as follows. limx→2 1-x2=1-22=1-4=-3   Thus, limx→2 1-x2=-3.…

Q: Use the Squeeze Theorem to show that lim x? cos (Hìnt: cos < 1 = 0

A: We have to find

Q: F ind the limit using L'Hopital Rule. lim 4 - 16 3x-16

A:

Q: limf(x) does not care what happens While a limit exactly at x = c because the limit is concerned…

A:

Q: lim -1 x→0+

A: Separate the limit.

Q: 5. Use the definition of limit to prove that lim[(x – 1)(sin x²)] = 0

A:

Q: 5. Find the limit, if it exists. If the limit does not exist, explain why. sin x - cos x (a) lim…

A:

Q: 40. Prove that lim Vx esin(7/x) = 0. 41-46 Find the limit, if it exists. If the lim explain why.

A:

Q: 1 - cos h Investigate lim h-0 numerically or graphically. Then h2 prove that the limit is equal to…

A: The limit to evaluate is  limh→01-coshh2 To find the limit numerically calculate the values of…

Q: 5. Evaluate the limits using any of the methods you know. Show your work. 1-cos 2x а. lim x-0 4sin2x

A:

Q: Determine the infinite limit. limit as x approaches 3 from the right side of ln(x2-9)

A: We have ln(x2 - 9 ) if we take x as √10 which is approximately equal to 3.16, then, x2 - 9 =1…

Q: Prove the limit as x approaches -2 of f(x)= 10x + 19 is -1 using the definition of a limit of a…

A:

Q: Evaluate. (a) limit as x goes to 0 -&gt; (tanx)/(2x) (b) limit as x goes to 5 -&gt; (-1)/(x-5)2 (c)…

A: a) The limit can be evaluated as.

Q: A function is defined by: In( x- 1) f (x) =- 1-x a) Using L'Hopital's rule, show that: lim f (x) =0,…

A: Critical points

Q: Using the elpison delta defination of a limit prove that the limit of (5x+7)=2 as x approaches -1…

A: Given function is  f(x) = 5x +7

Q: If lim f(x) and lim f(x) exist but are not equal, then x = c is a(n) jump discontinuity. X-C- XC+ If…

A:

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: To show that the given function is continuous using the limit definition

Q: 3. Evaluate the limit if it exists: а. lim 8-0 sin-B b. lim(1+x*)*

A:

Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim x→1 x´ +x –2 2

A:

Q: Evaluate the limit: lim --> 0 (ex+3x)1/x

A: It is an indetermined form of questions in case of limit. Which will be solve easily by below given…

Q: Suppose f is continuous on the interval (0,3). Assume further that f(0)= -2 and f(-3)= 5. Also, lim…

A:

Q: S 2x² f(x) = 8 - x for x 2 Compute the left- and right-hand limits at x = 2 and determine whether ƒ…

A:

Q: 5) Prove that the order of iteration of limits can be significant by showing that х2 lim(lim у-0…

A: It is needed to prove that order of iteration of limits can be significant by showing that:

Q: 1c. Use L'Hopital's Rule to find the Limit: lim          (1 - x)tan(pix/2) x-&gt;1-

A: We will use tan z = 1/cot z formula

Q: 44. Prove that if lim f(x)= L #0 and lim g(x)= 0, then the limit lim 8(x) does not exist.

A: Given: limx→cf(x)=L≠0 and limx→cg(x)=0 To Show- limx→cf(x)g(x) doesnot exist. Theorem- if limx→au(x)…

Q: A function f has a removable discontinuity at x = c if limf(x) exists by f is not continuous at x =…

A: Here, the given function is: f(x)=x-2|x|-2 So, function is not defined at x=2,-2

Q: and b at where? ] Use the &-8 definition of the limit to prove lim(4x-3)=5. X2 Find the & value When…

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Q: Now consider f(x) = ! defined for all real numbers except for x = 0. Appealing to the e-8…

A:

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: NOTE: Refresh your page if you can't see any equations. . find the limit of the function at x=-1

Q: 6 -- if a - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

A:

Q: If a function is continuous everywhere, its domain is all real numbers. If the limit exists as x…

A: The given statement is

Q: 2. Evaluate the limit by Use the definition of the derviative to compute the derivative of f(x) = 1…

A: Given,

Q: Prove using the definition of a limit. lim x→2^− (1/((x^2) − 4)= +∞)

A: Prove that   limx→2-1x2-4=∞

Q: 4х + 1 Let f(x) = X-2 (a) Use the precise definition of the limit (i.e. e, 8) to prove that lim f(x)…

A: To solve this question we need to apply the conditions of limit and continuity

Q: Let f be the function 7x + 1 for x 6 Compute the left- and right-hand limits at x = 6 and determine…

A: