x-1 1) Evaluate lim · x→1 yx-1

Q: Calculate each of the limits in Exercises

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Q:Prove that: Vi+x+x² -1. Lim- 12-2 cos x + lim x->T/4 sin(x - T /4) > log, 0.005

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Q: a. limr→0 cos(x) b. limx→n

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

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Q: 7. et² -e-y² = }(e - e-1) lim %3D (x, y)→(1,1) x+y

A: To Determine: to prove  lim(x, y)→(1, 1)ex2-e-y2x+y=12(e-e-1) Given: we have a  problem based on…

Q: 1 2. lim cOs X -

A: The given function rewrite as

Q: -xy lim (x,y)→(0,0) x²+y2

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Q: 1-coskx 2. lim kx = 0.

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Q: Q3) Find: (1) lim, 1+cos 2x (2) limx→-2- (x + 2) |4-x²| 2-x

A: Q3)1Here, we need to calculate the limit of ,limx→π21+cos2x4x-π2

Q: 25-и-5 e. lim u-0 vi+u-1 f. lim (3x² + 1)-2 x--00 2x? g. lim X+0o x²+1 x3+x

A: To evaluate the limit: e). limu→025-u-51+u-1 It is 00 form. We will evaluate the limit using…

Q: b. lim cos(x)-1 x2

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Q: x4-16y+ lim (x,y)¬(2,1) x²–4y2

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Q: 3* Evaluate (a) lim sin y and (b) lim y x-1 Vx +5

A: we have to evaluate the following: a)  limy→π3 siny b) limx→-13xx+5

Q: (a) lim sih 7x (b) lim x 0 sin 7x x - 9 (c) lim x-9 x - 3

A:

Q: 2 sin? x lim х-0 5x(1+сos x)

A: Let L=limx→ 02sin2x5x1+cosxlimx→ac·fx=c·limx→afxL=25limx→ 0sin2xx1+cosxPlug in the value…

Q: Find Lim-0.0 (r² + y²) In(x² +y²) '(xy)(0,0)

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Q: + h 4 (a) Lim×-1'x+1 X (b) Lim h→0 V5h + 4 – 2 -2 - t3 – 1 3. (c) Lim t-1 t-1 II

A: To show the given limits, we use the algebraic indentity and rationalization of a fraction.

Q: (a) lim 1-cos() 3x (b) lim xe 1/x (Hint: xe

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Q: -xy س3: أحسب lim (x,y)→(0,0) x²+y² إضافة ملف

A: See the attachment

Q: |z²–1| 2 1) Use a tble of functional values to evaluate: lim I-1

A: The tables containing the functional values are very useful to approximate a limit. The tables are a…

Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

Q: lim (x,y)-(-3,4) (x³ +3x²y² - 5y³ +1)

A: Here we have given an expression with limit and we have to solve it. We have lim (x,y)→(-3,4) (x3 +…

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

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Q: Зx +3x+5 х +2 1-cos.x (а). lim (b). lim

A: To evaluate the limit, limx→∞3x3+3x+5x3+2, plugin the limit and obtain the indeterminate form of the…

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

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

Q: (3) Evaluate lim -(1+sin(4))t dt

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Q: Prove the limit doesn't exist

A: cc

Q: 1 1 7. lim X-0 (Arctanx)² x2

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: 3* Evaluate (a) lim sin y and (b) lim x→-I /x + 5

A: To evaluate: a) limy→π3 sin y b) limx→-1 3xx+5

Q: Evaluate lim (2+ y) sin(x). (x,y) → (1,6) 02 O O o O Does not exist

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Q: find

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Q: .2 lim (x,y)→(0,0) x² + y²

A: Consider the given: limx,y→0,0x2x2+y2Let y=mx

Q: 1 1 dz = lim V3(w + h) – 2 V3w – 2 h 1- dw h-0

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Q: -xy اس3: أحسب lim (x,y)→(0,0) x²+y2

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Q: Along the path x = e" %3D find y +4xy lim (x,y)-(1,0) 3x – y - 3 does not exist O -2 -3 2 0 3

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Q: QUESTION 9 x²y along the path y =3x2. Find lim (x.y)-(0,0) x+y?

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Q: 1 1 +x+1 h 4 (a) Lim (b) Lim h-0 V5h + 4 –- 2 5 t3 – 1 (c) Lim- = 3. t-1 t- 1 II

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Q: xy + 1 lim (x, y)→(1, −1) x² − y²

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

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Q: 4xy lim Compute the (xy) (0,0)

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

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Q: Let h(x)

A: Consider the given function and its graph as hx=x2   x&lt;23x=22x&gt;2

Q: 68. (x) = sec x %3D lim a. As x- f(x)→ b. As x→2 f(x) → /2

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Q: 2* – 1 x→0 V1 +x – 1 lim Evaluate

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

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Q: (b) lim æ In(x² + y²) (x,y)→(0,0)

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

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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.