x²+1 lim tan (x,y) → (0,1) x? +(y-1)². O is equal to 0. O is equal to -II

Q: (а) lim 1-cos() 3x 1/х 1/х (b) lim хе 1/х (Hint: хe x+0"

A:

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

A:

Q: Find the one-sided limit

A: limx→12-x secπ x Now secπ x tends to ∞ as x tends to 12 from the left side.

Q: lim (x,y)→(0,0) (x² + x²) (х, у) ->(0,0) а. 0 b. 1 с. 1/2 d. Does not exist

A:

Q: lim cos x→0+

A: Given lim×-0 cos (1/x) For the above limit we have to solve it first

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

A:

Q: 5. lim tan x cos y = 1 (x,y)→(,0)

A: To show :  lim(x,y)→π4,0tan x cos y = 1

Q: Find the limits

A: Given: Function  To Find: Limit of the function at the given point

Q: lim (x,y)¬(0,0) cos-1 (*-xy x²+y²

A: Given

Q: lim (x, y)-(0,7/4) sec x tan y

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 -1 x+1 tan t sec 2t lim 3t

A: We know limx→0tan xx = 1 limx→af(x)·g(x) = limx→af(x) · limx→ag(x)

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

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Q: 1) limy-o 2ytan(1/y) sin(r-0²) 2) lim2n 101-Va 2 3) limg-n/2 (n²-482 )sec\ß] tan2x 4) lim T

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Q: lim (4 + (x + y} ) In(x² + y)) (х.у) - (0,0)

A:

Q: sin 3y cot 5y Q7// Evaluate limy→o° y cot 4y

A:

Q: Find the limit

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Q: tan2(3 + Ax) – tan? 3 (c) Compute lim by interpreting it as a derivative. Ar+0 Ar

A:

Q: lim (4+ (2? + y°) In(x² + y²)) (1,y)(0,0)

A: Given; lim(x,y)=(0,0)[4+(x2+y2)ln(x2+y2)]

Q: ขน lim (x,y) → (0,0) x² +10y²

A:

Q: e-3sin z (c) lim x² (d) lim sin(rx) lIn (x – 1) x→1+

A: The given limit is: (c) limx→∞e-3sinxx2  To find the value of the limit.

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

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

Q: lim cos x + x cos a. 0 b. 1 d. does not exist

A: This question is based on Squeeze theorem.

Q: lim (-4 0 sin x x

A: Let ,I=limx→ 01sinx-1xTaking cross multilplicationI=limx→ 0x-sinxxsinxI=0-sin(0)0sin(0)I=00Which is…

Q: lim 15 cos() x→0+ 7x

A:

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: 4. lim-0 A. B. 1 C. sin D. Does not exist E. -1

A: We need to find limit.

Q: السؤال 1 lim iz?-z z-- z2-1 i o -i O 1 0 -1 O

A:

Q: lim (x,y)→(0,0) x3y is equal to----- x6+ y2 (a)1 (c)does not exist (d)-2

A: In the above problem, at the point (0,0) the function is not continuous. So, it is not possible to…

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

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Q: 21. lim (x.y)-(0,0) x2+y2 22. sin( x* +y?) lim (xy)-(0,0)

A:

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: Prove the limit statements

A: limx→0x2sin1x=0 Now since the range of sinx is -1, 1, therefore -1≤sin1x≤1⇒-x2≤x2sin1x≤x2 Now,…

Q: x+xcosx A: lim x-0 sinx cosx tan2(3x) B: lim x-0 x² 1-tan?x C: lim zcosx-1)

A:

Q: lim x (1 – cos X→-0

A: limx→-∞x1-cos1x

Q: lim (1,4) (0,0) x2 + y2 Prove that

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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: 4+ sin x d. lim - 1- i cos(x+x) +2 g. lim

A: To find out the limit, substitute 0 for x and find out the limit value

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: e* + e-x – x² –- 2 lim sin? x – x2 х — x→0

A: To evaluate: The limit limx→0ex+e-x-x2-2sin2x-x2. Calculation: Use L'Hospital rule to evaluate the…

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

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

A: