2) fle -2x 22 アー4nt6 6) lim F(x)=2 c) limfe) Xー→2t こ doesn't exist a) lim f) = 2 %3D Xーラ -2

Q: By considering different paths of approach, show that the function f(x, y) has no limit as (x, y) →…

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

Q: What is lim x=inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^(3n)] + 2? (express answer as x,y)

A: Solve the following

Q: 1 x, and the line perpendicular to 6 Find the area of a triangle bounded by the y axis, the line f…

A:

Q: Estimate the limit numerically. ++7,000x³+ 800,000 lim 2x° + 1,269x³ 8. O to∞ 2.

A:

Q: Estimate f (2.1, 3.8) assuming that f(2, 4) = 5, fx(2, 4) = 0.3, f y(2, 4) = -0.2

A: Given : f2,4=5.fx2,4=0.3 , fy=2,4-0.2The linear approximation is :Lx,y=f2,4+fx2,4x-2+fy2,4y-4Now,…

Q: By considering different paths of approach, show that the functions in Exercises 41 have no limit as…

A:

Q: Find limx->∞,if for all x>5

A: We apply limx->∞ on all sides.

Q: The limit as x goes to zero of x-1 exists.   True or False?

A: We need to say whether the given statement, “The limit as x goes to zero of x-1 exists.” is true or…

Q: +2 dt 8. lim 7x

A:

Q: Prove that lim, = 1, (x > 0).

A:

Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2? (express answer as x,y)

A:

Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: 5. Differentiate using quotient rule: x+2 y x-2

A:

Q: 5. If lim f(x, y) = 5 (x,y)→(3,–7)" %3D for every curve C in R? containing the point (3, -7), what…

A: If limx,y→3,−7fx,y=5  is true, then it represents that limit exists atpoint (3,-7) for function…

Q: Explain why the paths y = mx and x = y² are suitable to check if the limit of f(x,y) = as (x, y) →…

A: *This question belongs to several variable (BSc problem) so I am solving it in Advanced math. *

Q: 1 1 lim xV1+x

A: limx→01x1+x-1x=limx→01-1+xx1+x

Q: Show that 2n lim n+2 = 2,

A:

Q: 2) Find FCO), if it exits Punctien f(z) - 2 if x raticnal if x irraticnal

A:

Q: x² – r3 lim - 2x2 + 3

A:

Q: Use the results of Section 2.3 to evaluate the limit lim e3×(x² – 6) =

A: Given that limx→0e3xx2-6 evaluate the limit

Q: 15. Differentiate using quotient rule: x+2 y = х-2

A: Given, y=(x+2)/(x-2) Then,dy/dx will be

Q: Let fx) = mx + b where m and b are constants. If lim fx) = 1 and lim Ax) = -1, determine m and b.

A: Given: fx=mx+b And limx→2fx=1 and limx→3fx=-1

Q: Point X is equidistant from F and T. Furthermore, point Y is equidistantfrom F and T. Does that mean…

A: To check: Whether the point X and Y are equally distance from F. Given: The point X is equidistance…

Q: Find the limits in Exercise

A: Given, limx→-12x3-5x2+3x+5 function is continous so find limit of function at x=-1…

Q: You are not allowed to use L'Hospital's Rule 2x2 – 32 - lim V3x + 4

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: By considering different paths of approach, show that the function f(x,y) has no limit as (x, y) →…

A:

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show…

A: We will find out the required value.

Q: Txーt e lim 4x² 4,2 +4x

A: Given that limx→0 e2x-14x2+4x We have to find the limit using L-Hopital rule L-Hopital's rule: If…

Q: What is the maximum point of the function f (x) = x² - x on the o terval [-2,2]?

A:

Q: 3. In your own words, explain the Squeeze Theorem.

A: Squeeze theorem is a calculus theorem related to limit of a function

Q: 1. Can Rolle's Theorem be applied to y = (x – 2)5 on the interval [0, 4]? Justify.

A: we will see how to proceed

Q: By considering different paths of approach, show that the functions in Exercises 41-42 have no limit…

A: Hi! You have uploaded multiple questions. As per norms, we will be solving only the first question…

Q: Evaluate the limit: lim 3z4 – 8z = - %3D Z - 1

A:

Q: How do I use the limit of laws when there is a square root in the numerator of the fraction?

A: We can explain through an example

Q: Use the results of Section 2.3 to evaluate the limit lim e5x(x2 – 10) =

A: By product law,  limx→afx×gx=limx→afx×limx→agx

Q: 1. Can Rolle's Theorem be applied to y = (x – 2)3 on the interval [0, 4]? Justify.

A: Check differentiability at x=2

Q: By considering different paths of approach, show that the functions in Exercises 41-42 have no limit…

A:

Q: 2) G VALUATE THE UMIT, IF IT EXISTS. Lim X-3 x2-X-12 uT x²+ 3x 2)

A: Given:         limx→-3x2+3xx2-x-12   Factoring                   =limx→-3xx+3x-4x+3

Q: 2. Using both a picture and words, explain the Squeeze Theorem.

A: Given : The Squeeze Theorem.

Q: is lim (sec x)ot æ 2

A: Apply exponent rule

Q: Evaluate the limit 5y5 – 4y3 + 2y² lim 7y4 + у3 + 2у

A:

Q: Find the limit. 4et – 4 1 + t – 1 2 - - lim 1 + t,

A: When limit is of the form 00 or ∞∞, then L'Hospital rule is used. In this rule,take the derivative…

Q: lim sec(4+x?)' Ax where Ax = 12-(-3) and x; = -3+iAx.

A:

Q: 7 Find a limit equal to V4x – 3dx. 3

A:

Q: Find the limit. 7) x6- (x - 6)2 lim A) -- B) = C) 0 D) -1

A: here option b is true

Q: Find the limit:    limx 2(4x2 + 3).

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.