cos x2 - 1 2. Find lim→0 2x 81,341 123

Q: lim (- %D x2 – 2 sinx + 2x - 1 42 30

A:

Q: 2. 2xy lim (x.y)-(0,0) x² + 2y6

A:

Q: tan?x lim

A:

Q: Q4: A) solve: 1+rsin 1) lim y-0 1+xcos

A: Given: limy→01+xsin1x1+xcos1x

Q: Find: tanx-sinx d) lim x3 4.

A:

Q: sin(1 – t) |2 – 2t| (b) [8 marks] lim t+1-

A: this is left hand limit then limit approaches from left side

Q: -xy lim (x,y)→(0,0) x²+y2

A:

Q: 2t lim -0 tan t

A: We have to find the following limit: limt→02ttan t

Q: lim, 1 f(x) = %3D

A: limx→a f(x) =L if and only if limx→a- f(x) = L =limx→a+ f(x) .

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: et - e- е limr0 2 sin x

A:

Q: 8r + 5tant Find lim t>0 sint

A:

Q: (t³ + 8)-dt + 8)-šdt lim

A:

Q: Find lim. Sin (X/y X-T/4

A:

Q: Vx+4 -2 1 limx¬0 ||

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Vx+2-3 (a) lim x→7 х—7 4x +3x – 10 | (b) lim х> -2 х* +8х +12 sin xcos x (c) lim x→ 0 x(х + 6)

A:

Q: tan (xy) = ? lim (х, у) ->(1,0) у + 2хy

A:

Q: Find lim 1+1? 1-e24 -2t -1 tant, 2 2 1-1

A:

Q: tan(x) d. limx→ x-5 e. limr→∞ xe-*

A:

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: 2-y lim 7+ 6y² y-

A:

Q: ex+e¬x_x²-2 3. lim X--0 SIN²X-x2

A: The given limit  limx→0ex+e-x-x2-2sin2x-x2 This limit is in 0/0 form, so we can apply L' Hospital's…

Q: Q2) A) 1-VI+1 sinax 3) lim I+1 1) lim 2) lim

A: Given that:                       (1)limx→∞x+1x2+3 (2)limx→01-x+1x(3)limx→0sin3xx   NOTE: As per our…

Q: Along the path x = e find lim (2,y)→(1,0) y²+6zy 3x-y-3

A: To evaluate the given limit: lim(x,y)→(1,0)y2+6xy3x-y-3 along the path x=ey. Here,…

Q: (iv) Find lim r 2ª – x² sin

A: Limits

Q: 4x(1 — сos(x)) lim х — sin(x) х>0

A: Because the limit is in 0/0 form. Apply L'hopital's rule.

Q: 8x+4-4cos?x+tanx Q1) Find lim X-0 4sin2x

A:

Q: (2) limuy)-(0,0) In(1+x²y®) =,

A: When we put x=0 , y=0 in the function we donot get indeterminant form so we can put the values…

Q: Along the path x = e' find y²+6xy lim (x,y)→(1,0) 3x-y-3

A:

Q: 2. メー gu)= - fex) = X üls Is1 3メ-1 احب lim (fog) x メー

A: We have to find limit

Q: Evaluate limx=0+ e(1/x)

A:

Q: . What is lim tan(x)? Why? 2 AY 10 8 6 4 2 -1A -0.5 0.5T, 1.57 27 2.57, 37 -4 -6

A: 1) limx→π2+tan(x)=? 2) limx→0+f(x) =? and limx→0-f(x) =?

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

A:

Q: d) lim cos x sec (5x)

A: The given expression is :  limx→π-2cosx sex5x  Let,  x+h=π2  As x→π-2 so, h→0  cosx sec5x=cosπ2-h…

Q: Q: find lim 1-cosz

A:

Q: Q1) Find lim Bx+4-4cos²x+tanx x-0 4sin2x 10x2+125-5 Q2) Find lim x-0 3x2

A:

Q: tan(xy) lim (х, у) -(1,0) у + 2ху 1 (с) 3 (d) 4 (а) 0 (b) (е) 1

A:

Q: tan ( xy) :? lim (х.,у) -> (0,1) х-y+x 1 (e) (d) - (а) 0 (b) 2 (е) 1 4

A:

Q: (b) Find lim, 0 xª cos 2.

A:

Q: nx + 1 If lim エ→+0 = 9, find n. 1 %3D nx -

A:

Q: 1x+21 Ex.2: lim ダー→ -2 (x+3) x+2

A: limx→-2-(x+3)|x+2|x+2

Q: tan(xy) = ? lim (х, у) >(,0) у+ 2ху 1 (c) 3 (а) 0 (b) (d) (е) 1

A:

Q: x2 – 1 t(2) = 1 What is lim t(x)?

A:

Q: tan(ху) = ? .2. (х,у) >(0,1) х*y+x lim

A:

Q: 3+2r lim エ→0 =?

A: Given , limx→03x2+2xx

Q: Inx 1 13. lim, X,

A:

Q: steps: -x*-5x lim arctan 4+3x2-2. V1+4x6 b. lim lim (V9x2 + 2x + 3x) С.

A: Solving by limit theorem we have

Q: (cos(3x+ 1))² lim 7+ 4x

A: our objective is to find the limit

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

A: To findlim(x,y)→(0,0)(x2+y2)ln(x2+y2)

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.