Along the path x = e y +6xy find lim (x.y)→(1,0) 3x-y-3 Along the path x = e y? +6xy ind lim (x,y)→(1,0) 3x-y-3 O -2 O -3 O 2 does not exist O 3

Q: f(x) = { cos x, xpi  which lim does not exist

A:

Q: ,- 3y sin (4x) - 3y - 2 e sin (4x) Find lim - 4x (х,у)—> (0,0) - 2 e sin (4x) lim - 4x (х,у) — (0,0)…

A:

Q: cos x dx - In (1 +x) 1- cos x a) b) lim

A: Given: a)∫011-cos xx2dx b)limx→0ln1+x21-cos x

Q: x2 – 1- y lim (x,y)→(1,0) X – Vy +1

A:

Q: 1-cos2 (x+y) 3. lim (xy)-(0,0) (r+y>)ety

A:

Q: 4. Proof Prove that lim x"y" dx dy = 0. n→∞

A:

Q: lim ( + y) In (² + y?) (z.y)-(0,0)

A: We can write the above expression as following :' x2+y2lnx2+y2=(x4+x2y2)lnx2+y2x2. Now, if we put…

Q: cos x ln(x - *) *-+ In (e-e*) 6. lim

A: Topic:- limits calculus

Q: 1. lim cot-1 (e*). 2. lim sech (ln x) x-0 S(x) = sech z

A:

Q: lim (x,y)¬(0,0) cos-1 (*-xy x²+y²

A: Given

Q: Hello, I need help with #29, evalute the limit.  Thank you.

A: Subtract them using LCD.LCD= tsqrt(1+t)

Q: 3 sen y lim (xy)-(3,0)

A: Since lim(y tends to 0) sin( y)/y=1 Therefore, lim(x,y)tends to (3,0) x^3sin(y)/y=(3)^3×1=27

Q: Find lim "(x.y)→(0,0) (4 + (x² + y? ) In(x² + y² )) Dose not exist O 1 4

A:

Q: Show necessary computation x²-9y? lim (x,y)→(1,0) tan-1 (x4 – 4xy + y²) lim (х,у)-(0,0) х-Зу b. а.…

A:

Q: 13) lim (n z 2-70 24) lim e- é- ース x - sinx 34) lim (Csx - Cotx)

A: Wherever applicable we used L'Hopital rule

Q: sin 3y cot 5y Q7// Evaluate limy-0 y cot 4y

A:

Q: lim f(x) vs f(-3) а. x--3 b. lim f(x) vs f(-1) x--1 c. lim f(x) vs f(1) X-1 d. lim f(x) vs f(3) X-3…

A:

Q: lim (x,y)→(0,0) In(2 + x² + y?) x² + y?

A:

Q: lim (x,y,z)→(-37,2,–1) (cos(xz) + In(xyz) – x/37) (2т — 2)у (z,4)→(1,0) (x – 1)² + y² xy? - lim lim…

A: Given lim(x,y,z)→(-3π,2,-1)cos(xz)+ln(xyz)-x3π lim(x,y)→(1,0)(2x-2)y(x-1)2+y2 lim(x,y)→(0,0)…

Q: i) lim(In (3x– 2)– In(5x+4)) Зх +1 lim 1 j) x0* sin x k) lim (csc x- cot x + cos x)

A:

Q: x 0+ (d) lim (1 – 2x)¯4" -4x x→0+ (e) lim (sin æ)-In æ (f) lim (– In æ)*in æ sin x

A:

Q: 2sin x lim -0 e - 1 lim - 5 cos x o e - x - 1 4 - 4e* lim -0 xe

A: As per our guidelines, we are allowed to answer the first question only please resubmit the other…

Q: (d) lim sinh(x) X+ -00 (e) lim sech(x) X+ 00 (f) lim coth(x) X+ 00 (9) lim coth(x) (h) lim coth(x)…

A:

Q: .2 lim (x, y) (0,0) along y = x2 |3|

A: Substitute y=x2 in the function. Now the limit becomes

Q: 71. Prove the reduction formula tank x dx = tan" k-1 х | tank-2 x dx k – 1 Hint: tank x = (sec² x –…

A:

Q: Find the limits

A: Consider the provided expression, limx,y→0,4xy Find the limit of the provided expression.

Q: a) x- y x*e cos( lim b) lim (x,y) (0,0) sin x+sin y (x,y) (0,0)

A:

Q: 1 - cos b. lim COS x 1 x0cos x 1 20. a. lim x0COs x 1 a inil ol l

A: Given information:The given limit function is shown below:a)

Q: find the limit:  limx→∞ (ln x)^3 / x^2

A:

Q: In Exercises 9-14, evaluate the limit or state that it does not exist.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 5. Find the length of the curve x =y? +2} from y =0 to y = 3. In(5x+2). In 3x 6. Solve lim

A:

Q: Rewrite the following as one-sided limits as in Exercise 50 and evaluate.

A: To evaluate the limit. (a).…

Q: 1 d) limy-→0- e) lim,o (1+ r/n)" 1 f) lim→0 x +

A: L'Hospital Rule : If limx→af(x)g(x) is in the form 00 or ∞∞, then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: tan ( xy) lim 2. (x,y)→(0,1) x´y+ x (a) 0 (b) (c) (d) (e) 1 -/4 -3 || -12

A: This question is related to Differential Equations.

Q: (x+h)³-x³ lim h→0 h. sin(3w) lim w-0 2w sin(h)(1-cos(h)) lim

A: We know (a+b)3 = a3 + 3a2b + 3ab2 + b3 limx→0sin xx = 1 limx→01 - cos xx = 0

Q: lim (2,y)+(0,0) In(2 + x² + y?) x2 + y?

A: We have to solve given limit:

Q: Lim Cos t X-2SM X2

A: limx→2cosπxx-2sinπx

Q: x - 2 lim (x. -t0. 01 3 + xr x' - x'y+ xy-y lim (x, y-10. 0) 2x - y lim (x. yl-(0. 0) (x. -(0. 0) x…

A: The limit of a function is defined as the value of the function which is obtained when the values of…

Q: 1-cos (x-T) lim x→T(x-T)sin (x-π)

A: Given limit, limx→π1-cosx-πx-πsinx-π

Q: c) lim x-+0 tan 3x 1- Jx e) lim x 1-x g) lim(\n² +1-n)

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: tan( xy ) lim (x,y)→(0,1) x´y+x 2 |3|

A: Given function is limx,y→0,1tanxyx2y+x

Q: (1) limr-(n/2)-(tan x)cos x (2) lim,-o x-3(tan-x-x) (b) If у %3D 4u?-Зи + 2 %; и 3 е* + 2e2х, find…

A: For other questions reupload according to bartleby guidelines

Q: Find the limits

A: Given,                     lim(x,y)→(0,ln2)ex-y     And we have to find its limit.

Q: lim (z,y)→(0,0) (2+(x² +y²) In(x² + y²))

A: We have to find the limit of: lim(x,y)→(0,0) 2+(x2+y2)ln(x2+y2)

Q: j) lim e- =

A: 2. (j). We have to find the limit:  limx→∞ e-x

Q: Show that (x + 1)² sin y lim (x,y)→(−1,0) (x+1)4 + y² does not exist.

A:

Q: If f(x) = xcosx then limf(x+h)-f(x) h COSX = ? %3D %3D h-0

A:

Q: lim(x,y)->(0,0) = (1+x2+y2-cos(x2+y2))/(x2+y2)

A:

Q: ex+y (²+x*)siny Зх - 2y П. lim III. lim (x,y)¬{0,0), lim 2 x* +y" (х.у) -0,0) 1+e*-у (x.y)-0,0)

A: We have to solve given problem:

Q: 2x e* –1 lim- x→0 sin (2x)

A: Since you have asked multiple questions in a single request, we would be answering only the first…