Let a, b, c€ R. Then max{a, b, c)= max(a, max(b, c}}. Select one: O True O False lim(xn) = x is necessary and sufficient for lim(]x,- ×|) =0. Select one: O True O False Let f, g: D→ R be bounded functions on D. If f(x) s g(y) for all x, y € D, then inf f(D) s sup g(D). Select one: O True O False The set S=[-1, 2]U[3, 5] is an interval. Select one: O True O False

Q: evaluate the limit

A: Given that: The limit is limx→0 1 - 2x1x .

Q: ry Let f(r, y) and let L = lim(z.1) >(0,0) f(x, y). Which of the following statements is correct?…

A: Third option is correct.

Q: f(x): = ax² + x - b, ax + b, 2ax - 7, (a) Find the values of a and b such that f is continuous on…

A:

Q: O Find the limit if It CXIISES #7A Lim 14x +lx-71) #7B If 3x-UEflx)-8 #7D %23

A: Substitute x=7 in the expression

Q: If it is continuous, there are 3 conditions needed to be satisfied: i. f(a) is defined ii. lim x→a…

A: The three criterias that you have mentioned are for a point. When we check the continuity at a…

Q: Find the limit of the function along the path y = 0. X-m lim (х.у) - (0,0) у -п C. -" 772 772 A. 0…

A:

Q: This is somewhat confusing A function f : (a,b) → R is uniformly continuous if and only if the…

A: Given: f:a,b→R be a uniformly continuous function. we have to prove limx→bfx exist. Let bn be a…

Q: lim 극 et – 1 x-1

A:

Q: Use l’Hôpital’s rule to find the limits

A: We have to find the limits of the function by L'Hospital's rule: limt→∞et+t2et-t If we limits are in…

Q: lim f(x, y) = 6, then f(1.9, 2.9) = 6- %3D (x, y) + (2, 3) If f(4, 5) = 3 Vf(4, 5) = (-3, 2) then…

A:

Q: Let f(x) = a² + 3. Find lim * + h) – f(x) h→0 h Select one: O a. 0 O b. 3 O c. 2x+3 O d. 2x

A:

Q: Let A.=(-11.1- and B. 4. for all n E N. 1. PL lim PL(A) 2 BUB. =2 3. AL lim u(A.) -3.

A:

Q: Solve using method of undetermined coefficients: y" + y' - 2y = x². %3D

A: Solution :-

Q: (d) lim 1-0 1 +3 - 3/1 I

A:

Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

Q: 31. If f is continuous and f(3) = 9, which of the following statements must be true? (A) lim f(3x) =…

A: Here we define which statement is true or false.

Q: 10. Use the definition of limit to show that a. lim (x² + 4x) = 12, Z-2

A:

Q: AntAlmanac Grades for Zainab T. Suppose fand g are continuous functions such that g(9) = 5 and lim X…

A: If f(x) is continuous at x=a then limx→a f(x) = f(a) .

Q: ху — 2х — у +2 lim (K. y)-(1,2) X* + y² – 2x – 4y + 5

A: Let  S  be an open set containing  (x0,y0) , and let  f  be a function of two variables defined on…

Q: 1). Does the left-side limit of the difference quotient of the function g(w)=|w| exist at w=0? If it…

A:

Q: If lim f( x ) + f(a) ,then f(x) is at continuous , y = f(a) not continuous ,x = a continuous, x = a…

A:

Q: 5. Calculate lim f(x), where x+1+ f(x) = = its 12.05 (c)-2 (d) 2 (e) does not exist 5A 5B if x 1 x-1…

A:

Q: lim(x, y) – (5,9)(÷ ) = ;

A: To show                limx, y→5, 9xy=59 using the epsilon-delta definition of limits. Pre-requisite…

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: