What is the limit of f (x) = 1 as x → T?

Q: What does it mean for a function ƒ(x, y) to have limit L as (x, y) S (x0 , y0)?

A: To show: "a function ƒ(x, y) to have limit L as x,y→x0,y0"

Q: if r = -1 Is f(r) = · continuous at r= - -1? (Show your work using limits.)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Show that the function f(x, y) x4 + y? has no limit as (x, y) approaches (0,0).

A: Note: Since we can solve at most one problem at a time, we have solved the first one. Kindly…

Q: What is the limit of f(x, y) %3D as x2 + y? (x,y) approaches (0,0) along the curve y = x?

A: Explanation of the answer is as follows

Q: Find lim (x,y,z)-(0,0,0) x²+y2+z4 xy+yz?+xz2 if it exists, or show that the limit does not exist.

A:

Q: If functions ƒ(x) and g(x) are continuous for

A:

Q: Find the limit. t2 j+ sin(7t) k sin2(t) -2t ¡ + lim t→0 e

A: We have to find the limit: limt→0e-2t i+t2sin2t j+sin(7t) k

Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: Find the limit. Enter DNE if the limit does not exist. lim (x,y) → (0,0) x² + 12y?

A: Given limit, lim(x,y)→(0,0)x2yx2+12y2

Q: Show that the limit x²ycos y lim (x.y)→(0,0) 2x4 +y² does not exist.

A:

Q: 2. Find the the limit. li -y 1 (tany): 2 Y- 2

A: Given that:                limy→π2-(tan y)π2-y

Q: Suppose f is continuous on [0, 1]. What is lim n→ ∞ 1 S fo 0 f(x) dx?

A:

Q: Evaluate f x2 dx using the limit defintion of the definite integral.

A:

Q: Find the limit of the function f(x, y) = 4e10z–3y (x, y) → (0,0). as lim (x,y)→(0,0) 4e10x-3y

A:

Q: Use a table of values to estimate tne value of the limit of lim Vx + 4 – 2 f(x) f(x) 2.

A: Consider: limx→0x+4-2x   Let fx=x+4-2x Since we have to calculate limit at 0 of fx=x+4-2x.  Make the…

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

A:

Q: Explain why the paths y = mx and x = y are suitable to check if the limit of xy f(x,y) as (x, y)…

A:

Q: 9. lim 15 1 + (i/n)6

A:

Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

A:

Q: Express the limit as a definite integral. [Hint: Consider f(x) = x".] lim 5 i = 1 1 dx

A: To express the limit as a definite integral, limn→∞∑i=1n3i4n5

Q: What does it mean for a function ƒ(x, y) to have limit L as (x, y) → (x0 , y0)? What are the basic…

A: What does it mean for a function ƒ(x, y) to have limit L as(x, y) → (x0 , y0)? What are the basic…

Q: Find the limit (2x + y)² lim (x,y)→(0,0) 4x² + v² (Enter dne if the limit does not exist)

A: WE CAN FIND LIMIT . So , we can find limit along the line y=mx .i.e, we can choose path.If for every…

Q: Show that the limit of the function f(x,y) = at (0,0) does not exist. (x+y)² x² + y²

A: Limit of a Function: Like a single-variable function, a multi-variable function can also have limit.…

Q: Find f'(a) using the limit definition for 1 f(x) = V6 – 5x -

A:

Q: Let f(x) = /20 – x. Compute f'(4) using the limit definition f'(4) - - Find an equation of the…

A:

Q: What is the limit of g(t) = t as t → π?

A: We find the limit by substitution

Q: Evaluate the limit sin(a – Vy) lim (2,y)→(1,1) x - y

A: Here, we will use the following formulas,

Q: X,xif limF,(t)= F(t) at all t for which Fis Continuous

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 7. Find the limit as x approaches 0. F V I 2 2 O infinity O limit does not exist Oo .

A:

Q: What is the limit of (In(e+h)-1)/ h at h=0?

A:

Q: Let f(x, y) = 2*. Find fy(1, 2) using the limit definition.

A:

Q: Find the limit of f(x) as x approaches 2, where

A: fx=1,  x≠20,  x=2

Q: Find the value of a for which the limit sin (ax) – sin x – x lim x→0 is finite and evaluate the…

A:

Q: . Apply the two path test to make sure the following limit exist or not at (0,0) xy f(x, y) x³ +…

A:

Q: Show that the limit xłycosy lim (x.y)→(0,0) 2x4 +y² does not exist.

A:

Q: Show that the function f(x, y) xy? – 1 has y – 1 no limit as (r, y) → (1, 1).

A:

Q: If f is a continuous function and F'(x)=f(x) for all x € R, then - x)dx=?

A:

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

A:

Q: What is the limit of f(x) = 5 as x approaches a? (If an answer does not exist, enter DNE.) dne Need…

A: Solve simply

Q: Find Ilim(x,y) → (0,0); x² + y² whether the limit exists or not

A:

Q: If f(z) is continuous at z then it must be differenttiable at z, 0.

A:

Q: . Is f(x)= Vx + 1 continuous at x == -1? Yes, because all functions are continuous No, because the…

A:

Q: Show that f (x, y) = has no limit as (x, y)→(0,0) Vx2+y2

A: The objective is to show that f(x,y) has no limit as (x,y) approaches to (0,0).

Q: Find the limit of f(1,y) = as (r, y) approaches (0,0), if it exists. If it does not exist, show why.…

A:

Q: F(x) Let F(r) = | 3e" dt. Find lim if it exists. If the limit does not exist, explain why.

A:

Q: what is the limit of f(t) as t approaches 3. F(t)= ((1/t)-1/3)/t-3?

A:

Q: Find the limit of (x3+x2)1/2sin(((2)1/2pi)/x) as x approaches 0

A: To find

Q: compute dy/dx using the limit definition. y = 4 − x2

A:

Q: Suppose that f(x) is a continuous function on the interval [0, T] . If f(x)=(sin x)ª for 0<x<T, then…

A: we have to find the value of given function. the solution is following.

Q: What is the the value of the limit lim,0 Vn (Vn+1- /n)? Show your work.

A: