3. Explain: The limit of a function f(x) at x = a can exist and the function can still be discontinuous at that point.

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: Use l'Hospital's Rule to find the exact value of the limit. lim x→∞ ((1 +(3/x))^x

A:

Q: Estimate the limit of the following functions from the left and from the right and then state…

A: We have to find the limit from the left and right.

Q: lim 1 + X00

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

Q: 1. What is the difference between a function whose limit does not exist and one that increases…

A: Definition of Limit: Let E⊆ R and f:E→R.  Let a∈R be such that ((a-r,a+r)    {a})∩E is non empty for…

Q: Find the value of the limit lim 1 1 X 1 In(x) X-1

A:

Q: Can we evaluate the limit using f(c) if the constant c will not make the function undefined or…

A:

Q: I'm supposed to evaluate the limit or show that it doesn't exist. The answer is supposed to be 16…

A: Given,

Q: How would this process look should we try to do it via limit definition (IE, (f(x+h)-(fx))/h)?

A: Derivative of g(x) at x=a=limh→0g(a+h)-g(a)h

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

A:

Q: Explain, using limit definition, why f′(x) = 0 for any constant function f(x) = c.

A:

Q: (2) Use L'Hopital's rule to find the limit. lim x

A:

Q: Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct…

A: let f(x)=xx

Q: Solve using L'hospital's rule:   Find the limit of (4x+1)^cot(x) as x approaches 0 from the right…

A:

Q: Find the limit of the function if it exists lim (x,y)+(0,0) x² + y² - 2xy y³ – x3

A: Given,         lim(x, y)→(0, 0)x2+y2-2xyy3-x3

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

A: 1st statement is TRUE 2nd statement is FALSE. Explanation is given below...

Q: a)! Find the limit or show it does not exist: xy³ lim x,y) →(0,0) x² + y²

A: Note: Since you have posted multiple questions. As per our guidelines we are supposed to solve one…

Q: lim 3 1. x+00

A: To evaluate the given limit.limx→+∞1-3xx

Q: Hello,  How do I know when the limit is since it is not going by pi/6, pi/4, pi/3, pi/2, pi, and 2pi…

A: As a first step I will respond to your specific question "What is the limit? Or how do i know when…

Q: Prove that limp-→3 x² = 9 using the epsilon-delta definition of limit

A:

Q: There was a question on a previous assignment I had trouble completing. I was unable to fully solve…

A: Consider the two paths y=x and y=x2 through the origin.

Q: 3. Let f(x) and let a>0. Using the definition of the derivative 2+Va as a limit, find f'(a). Your…

A:

Q: By considering different paths of approach, show that the function below has no limit as…

A: Given function f(x,y)=x4x4+y2 The objective is to show that the function has no limit as x,y→0,0.

Q: Find the limit: lim x° -1

A:

Q: Find the limit. If the limit does not exist, explain why. Vx-/2y lim (x,y)→(4,2) x-2y

A: Factories the denominator term and cancel out the common from numerator.

Q: Use the limit definition of the derivative f (x) – f(a) f'(a) = lim x→a Т — а to find f'(a) in each…

A: fx=3x1-x   , (for x≠1) We need to find the derivative of the given function using the limit…

Q: Find the limit: lim x° –1

A: The solution of the problem is given in the next step.

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A:

Q: By considering different paths of approach, show that the function below has no limit as…

A:

Q: Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct…

A:

Q: If f(x)f(x) is a function, explain what we mean by the derivative f′(x)f′(x). Answer A and B below:…

A:

Q: True or False? The limit of f(x) as x approaches ?5 is f(5?).

A: The given statement is,The limit of f(x)as x approaches 5  is f(5) is partially true, if the…

Q: By considering different paths of approach, show that the function below has no limit as…

A: We will consider the limit of the given function as (x,y)→(0,0) along two paths: 1. The straight…

Q: 2. Find the following limits, if they exist. (If they do not exist, but approach too, indicate this…

A:

Q: 6. By considering different paths of approach, show that the following function has no limit as (x,…

A: given f(x,y)=5x2yx8+y2we need to show that the following function has no limit

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: What are some examples where we could not directly evaluate the limit at the point the variable is…

A: The objective is to find some examples where we could not directly evaluate the limit at the point…

Q: Determine the limit by analytic methods. (You may round your answer to three decimal places.) Vx + 2…

A: lim x->0x+2-2x To find out the limit, we multiply the fraction by conjugate of numerator lim…

Q: By considering different paths of approach, show that the function below has no limit as…

A: Since you have asked multiple questions, we will solve first one for you. If you want other question…

Q: for the limit lim x->infinity (x^2/2^x) i am supposed to create a table of x at…

A: Created the table using the equation and calculator.

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

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Use L-Hospital Rule to find the limit as x goes to infinity (1-(3/x))^(2x).

A:

Q: Tim X csc(Tx) X+1

A:

Q: Tet メni 2+Xn- show thal xn is convayas. Fend the limit. Conve

A:

Q: Use a table of values to estimate the value of the limit. If you have a graphing device, use it to…

A:

Q: exV – 1 Let g(x,y) (a, b) = (1,0). Show that lim g(x,y) does not exist. (x,V) - (a,b) %3D %3D x+y -…

A: Firstly it should be proved that limit does not exists and then recognize the two limit values so…

Q: True or False: 6. If the limit exists at x = a then the function is continuous at x = a. 7. A…

A: This question can be solved using the concept of limit, continuity and differentiability.

Q: sin(x) Comment - Knowing that the limit lim-0 = 1 means that for a reason- ably small interval of…

A: Given that: limx→0sinxx=1 Or, sinx≈x,  for  x→0.   We have to verify using Desmos to plot both…

Q: Examine if the following limit exists, x+y+1 lim (x,y) (0,0) In(x2 + y²) * If the limit exist,…

A: Given               lim(x,y)→(0,0)x+y+1log(x2+y2) Here we can Replace y=x and x tends to 0 as well…