2) By using E-S definition of limit, show lim (x+y+xy)cos÷ cos 음-0 COS (xy)(0,0)

Q: is it true that ∇f(limx)=lim∇f(x) and further that ∇2f(limx)=lim∇2f(x)?

A: We know,  ∇f(xi)=f(xi)-f(xi-h), h=xi-x0i,i=0,1,2...And…

Q: Find lim (1 + sin5x) cot3x x-0+

A:

Q: Suppose that f(x, 0) = 3 for all x ≠ 0 and f(0, y) = 5 for all y ≠ 0. What can you conclude about…

A: The limit of the function, f(x,y) at a point (a,b) does not exist if two paths upon which the…

Q: If f(x+y)=f(x)+f(y) for all x , y e R and E(tanx) _ 2f (sinx) f (1) =1,then evaluate lim x’f(sinx)…

A:

Q: Find Integral (cos(x) cos (2x) cos (5x) dx : considering cos (mx) cos (nx)= = (cos((m-n)x)+ cos…

A:

Q: If lim f(x) = = co then f (x) XCOS cos² X00

A: Given- If limx→∞fx=∞ then fx=xcos1x To Prove- The above expression.

Q: 2. Given the graph of the function f shown below, determine which of the following statements is…

A:

Q: Let f(x) = x² + 9, x > 0. Find lim f'(x) →25

A: f(x)=x2+9

Q: Let f(x) = V1– cos 2x a) f has a • discontinuity at 0. b) lim f(x) = c) lim f(x) =

A:

Q: Show that lim (2,v)>(0,0) **+y D0.

A:

Q: Ex x-2 XE3, X-2 12) Consider メレ3 2) lim. (f(x) b) lim. (f(x)

A: Topic:- limit

Q: **. (1) lim,- V1+cos 2x 4 (x-) Q3) Find:

A:

Q: Could the limit as xà1 of f(x)=(x+sinx)/(1+x+cosx) be found simply by substituting 1 into the…

A: Given function f(x)=(x+ sin (x))/(1+x+ cos (x)) Now we will evaluate limit of f(X) as X tends to 1…

Q: Find lim 1-CoS 3X Xう。 tan x -1 lim メー X - X->

A: Solution is given below..

Q: Find lim x+x:

A:

Q: Show that lim x|cos )= = 0.

A:

Q: Determine limx→−2 6/x-2, if it exists

A: limx→−2 6/x-2 yes limit exist and we can direct apply the limit so put -2 in given function…

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: Evaluate:- x+2 sin x 1: lim Vx +2 sin x +1-Vsin? 40 einf

A: Since you have asked multiple questions in single request.so we will answering only first question.

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.