5. If lim f(x, y) = 5 (x,y)→(3,–7)" %3D for every curve C in R? containing the point (3, -7), what can you say about lim f(x, y)? What can you say (x,y)→(3,–7)" about f(3, –7)?

Q: 2(x-1)* - y² Lex-1)* +2y (d) Show lim does not exist.

A: Limit exist

Q: Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the…

A: Given

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) approaches 1 as (x, y) approaches (0, 0) along the path y = mx, where m is any real…

A: To check whether the given statement is true or false.

Q: 7 sin(T2) In (zº) q(z) = %3D What is lim q(x)? ncwor bolow:

A:

Q: 4! find lim, B4,-2) S x approachesto I from postve direction.

A:

Q: Use the two-path test to prove that the following limit does not exist. x+ 2y lim (x.y)→(0,0) *- 2y…

A:

Q: Draw the phase portrait for i=2 -1. If z(0) = 1/2, what are the limits lim z(t)?

A:

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(7/2)-(tan x)" (2) limy-o…

A:

Q: V5+s-V5 lim s→0 S

A: lims→ 05+s-5s=lims→ 01s+5+5Plug in the value s=0=10+5+5=125

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

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

Q: Evaluate the limits in Exercise 7 and 8. cos t dt sin 8. lim x x→0+ 7. lim

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the value of the following limits: 5y 1-limy→o tan 10y 2-limx-0 6x cot3x 7x²+8x 3-limx-0 4x²…

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: パーy (x.y)-(0,0) x + y 2.) Prove that lim does not exist.

A:

Q: Use the Squeeze Theorem to show that lim a sin (1/r) = 0. Show all %3D work. 2.

A:

Q: Find the limit. lim (cos(t), cos(t), t In(t)) t-0+

A: Given: limt→0+cost, cost, t5lnt

Q: Compute the following limit along lines of the form y = mx, for m 0, and along the parabola y= x.…

A:

Q: Evaluate the limit: lim y-> 0 (1-cos 2y)/ (1- cos 4y)

A: We have to evaluate the limit                                            limy→01-cos2y1-cos4y

Q: Find the limit. lim (cos(t), cos(t), t* In(t)) t-0+

A:

Q: hey you didnt state the assumptions of the model and the limintations as well

A: To state: Assumptions and limitations of an exponential model.

Q: lim is: X+ d X Does not exist

A: Use the definition of limit to solve this problem.

Q: Find the limits in Exercise

A: To find the limit  limθ → π6 sin θ - 12θ - π6

Q: Q1) A) Find the tangent equation for the function: f(x) = vx2 + 5 at =2 ? B) Find the limits by…

A:

Q: Find the limits in Exercise

A: Given : limh→055h+4+4

Q: (b) Show that lim (x.y)(0,0) 2x6 + y2 does not exist by letting (x, y)→(0, 0) along the curve y =…

A:

Q: [4] (a) Show that lim (xa)-(0,0) 2x+y? y-mx, or along any parabola y= exists and it's approaches to…

A:

Q: Find the limits. Enter "DNE" if the limit does not exist. lim cos (x.y)¬(0,0) x' – y' x² + y² 4x lim…

A: Find the limits : Given :            lim(x,y)→(0,0)cosx7-y7x2+y2               =  cos 0-00+0…

Q: 6. Figure out the following limits without applying L'Hopital Rule. sin(r- 4) V2r -1-1 b. lim (2²…

A:

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: x-y (x,y) →(0.0) x + y 2.) Prove that lim does not exist.

A:

Q: Find the limits by rewriting the fractions first.

A: We have to find the limit: limx, y→0, 01-cosxyxy Rewriting the fraction using trigonometric formula,…

Q: Compute the following limit along lines of the form y = mx, for m 0, and along the parabola y = x.…

A:

Q: 1. a. Describe the level curves of the function f(x,y) = %3D x* + y b. Show that the limit lim (2,y)…

A:

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(n/2)-(tan x)cosx (2) lim,--0…

A: L'Hôpital's rule states that for functions fx and gx which are differentiable on an open interval I…

Q: Along the path a = e" find %3D lim (7,y) (1,0) y²-6ry 3r-y-3 O 2 O -2 O-3 O does not exist 0 3

A: we have to find the following limit

Q: The graph of fCx) below To evalvate tue following limits. Ao lim fex) 104 9. B. ling fCX) C.lim f(X)…

A: Given, graph of fxTo find: limx→2-fx limx→2fx limx→4fx limx→5fx limx→∞fx

Q: Shone that lim g (x,yJ-p (0,0) does not exist,

A: According to the definition of limit, we have

Q: 70. J, f(x) dx may not equal lim , f(x) dx Show that 2x dx o x² + 1 diverges and hence that 2x dx x²…

A:

Q: (b) Show that lim (z.)(0,0) lim (z.)(0,0) does not exist. (c) Show that does not exist if +: 0, p…

A:

Q: Find the limit or prove that it does not exist lim (2,y)→(0,0) T° cos x + 2y sin y x2 + 4y2

A: We will evaluate the limit limx, y→0, 0x3cos x+2y3sin yx2+4y2  using polar coordinates.

Q: Q2: (a) By using " L' Hopital rul (1) limx¬(1/2)-(tan x)cos x

A:

Q: Зу Let flx,y) = , find the lim(xy)¬(-1,1)( Зу %3D x+y' ) along the curve y=x² .

A:

Q: (i) Prove that Lim Vent +1 1 1 + + + /2n²+n] ... V2n2+2

A: Given that, g(x)=limn→∞12n2+1+12n2+2+....+12n2+n from sandwich theoram we can say if f(x)≤g(x)≤h(x),…

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim 0 sin 2 -16 2. lim 4 (V+5)-3

A: 1. Here limx→07xsin 2x is of 00 form, so by applying L. hospital rule, we get limx→07xsin 2x =…

Q: Evaluate the following limits.

A:

Q: S, f(x) dr may not equal lim , f(x) dx. Show that 2x dx x* + 1 diverges and hence that 2x dx ? + 1…

A:

Q: thát limx,y)→(0,0) x6- dõés not exist by using the two-paths approach.

A: