1. Consider the function given by if x € QU [0, 1] if x € QºU [0, 1] f(x) = 1- I Determine if the following limit exist or not, and prove your claim. lim f(r)

Q: If the fucntion f is undefined at x then lim f(x) does not exist. = c, C, FALSE O TRUE

A: Given- If the function fis undefined at x=c then limx→cfx does not exist. To Check- If the above…

Q: Let S-6x2 + 6z for z 0. According to the alternate form of the definition of the derivative, to…

A:

Q: For a function f, suppose lim f(x) does not exist because the left – hand and right – hand limit…

A: Given limx→c f(x) does not exist because the left-hand and right - hand limit have different values.

Q: Find a value for the constant "a" that will make the function f(x) continuous. f(x) = { ax- if xs2…

A:

Q: and If lim f(x) = lim g(x) = +o and flx) =1 and gtxl = e, what is the limit of the division of !!…

A: As given limit is infinitely by infinity form so use L'hopital's rule and substitute the given…

Q: 1 Discuss the existence of the limit lim sin x 0 x

A: To determine: The limit

Q: If f(x) is differentiable at X =c then lim f(x) must exist and f(c) must be defined

A:

Q: Evaluate f(-1+h) – f(-1) lim where f(r) = 5z'+1. Enter I for oo, -I for -oo, and DNE if the limit…

A:

Q: - x² if x 3 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x…

A:

Q: Use the graph of the given function f to determine the limit at the indicated value of a, if it…

A: Graph of the function is given, we have to find the limit at x=a

Q: 1 (1+ h)² + 1 lim x-0 x2 – 1 lim h-3

A: limx→ 0x3-1x2-1Plug in the value x=0=03-102-1=1

Q: Solve the following limit by definition (ii) (4 – 2x, x 1 lim f(x) = 2 if f(x) = %3D x→1

A:

Q: 3. Can f (x) approach a limit as x → c if f(c) is undefined? If so,

A:

Q: Compute f(x +h) + f(x– h)- 2f(x) lim h-0 h2 for the following functions: (a) f(x) =x (b) f(x) = x2…

A: For the real function f, if f(a+h)-f(a)h has a limit, h approaches to zero. This limit is the…

Q: 9) Find the limit, if it exists, or show that the limit does not exist: lim (x,y)→(0,0) xª + 3y4

A:

Q: Please

A:

Q: Compute the limit 1 a2 1 - x2 lim xa x а - What can you say about the derivative of f(x) = ?

A: Given limit :

Q: Use the E-8 definition of a limit to prove lim Xy (Xy) →(0,0) x² +y²

A: Consider the equation

Q: We have the function if (x, y) # (0,0), xy x²+y² f (x, y) if (x, y) = (0,0), (а) Find lim…

A: We have to find the following given conditions according to the given condition

Q: Show that the following limit does not exist. ху lim (x. y)-(0, 0) 3x2 +2y2

A:

Q: If x4 <=ƒ(x)<= x2 for x in [-1, 1] and x2<=ƒ(x) <= x4 for x <-1 and x> 1, at what…

A: Summarizing the given information:             . We need to find out that at what points c, we…

Q: 2) If x3 s f(x) sx for x in [-1,1), find lim f(x) if it exists. x-0 A) 0 B) Does not exist C) -1 D)…

A:

Q: 2 Show that the following limit does not exist. lim Ty Cos y (r.9)-(0.0) 3r+ y²

A:

Q: Show that the limit does not exist. xy? lim (1,y)→(0,0) x³ + y6

A:

Q: 5) a) If a > 0, compute lim a¯*. b) Which approaches its limit faster as x→», y=2* or y=x²?

A:

Q: x+h-Vx 12. lim h

A:

Q: 1 Let f(x) According to the definition, 7 4x f'(x) = lim h0 (Enter the limit in reduced form) %3D

A: Givenf(x)=14x-7

Q: Find the limit       lim h approaches 0   [(5h + 4)^1/2   - 2] /h

A: We have to find the limit of the given function: limh→05h+412-2h Since it is 00 indeterminate form…

Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

A:

Q: Find the maximum value of & > 0 that satisfies the limit claim corresponding to e = 0.3, that is,…

A: In the question it is asked to calculate the maximum value of δ for the given function limx→59-x5=8

Q: - x – x2 if x 2 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

A:

Q: If a function f is not defined at x = a then the limit lim f(x) as x approaches a never exists.…

A: To check: Whether the statement is true or false: Given: The statement is " If a function is not…

Q: 1. Consider the function given by if r € QU [0, 1] f(x) = 1- I 1 ° if r E Q°U [0, 1] Determine if…

A:

Q: 2) Suppose that the limit of a function f(x) exists at z = a. If lim f(x) = M and lim f(x) = N, what…

A: Given:- f(x) exists at x=a We have to find the relation between M and N for given limit of a…

Q: Compute the value of the limit below by relating the limit to the definition of a derivative of a…

A:

Q: (a) Compute the following limits: (i) lim **+x²+x+1 x2-1 sec-1(vZ+h)-sec-1/2 (ii) lim h→0 h

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

Q: for all a E R \ {0}. Using the e-ð definition of the limit of a function, prove that lim Do not use…

A:

Q: 1. Evaluate the limit: xy - y lim (x, y) → (1, 2) x² - x+2xy - 2y

A:

Q: If xz? f (x,z) = x² + z4 Does limr2)a(0.0) f(x, z) exist? Find the limit if it exist.

A:

Q: 3. Compute the limit algebraically Vx +3x2 lim 6x 1

A:

Q: 2. Determine the value of the following limit along all paths through the origin for which x + -2y.…

A:

Q: et –1 t2 – 3t + 5 lim t-0 t t2 – 1

A:

Q: . For a function f, suppose lim f(x) does not exist because values of f(x) oscillate between two…

A:

Q: 3. Compute the limit algebraically Vx + 3x2 lim 6x 1

A: Solution: The objective is to find the limit of the given function

Q: Compute the lim as x goes to 0+ (e^x - 1 - x)/ (xe^x - x)

A: we have to compute the limx→0+ex-1-xxex-x

Q: Suppose that lim, →o(f(x) – 9(x)) = 0 and h(x) is a function with domain R. a) Assume that |h(x) –…

A: We will answer the first question as we only answer one question at a time. Please resubmit the…

Q: 27 Let f(z) = エー3 Find lim f(r). Enter I for oo, -I for - 00, and DNE if the limit does not exist.…

A: In this question we have to find the limit of the given function.

Q: 1.16 Let f(x) = lim_f(x) = H-4 2, 4x + 19, Calculate the following limits. Enter DNE if the limit…

A: