2х + 1 29. lim x² – x X→-∞ - sin 2x 31. lim

Q: 4. lim xy (xy)-(0.0) v2-e-1

A: To evaluate limx,y→0,0xy2-exy-1 Substitute t=xy, then as x,y tends to 0,0 implies t tends to 0.…

Q: - «) lim (2 – ez x→0

A:

Q: 9. Lim 6x - Sin 2x メ→0 2x +3sin 4X b. lim x²-1 1/2

A:

Q: 1. lim (x – 4)(x² + 8) x-5 2(t-10)² 2. lim t-10 5+x-4x² 3. lim X-0 v1+x242x*

A: (As per bartleby guidelines, for questions containing multiple subparts, only first three questions…

Q: 1- V1– x2 с) lim x→0 [without using l'Hospital Rule] x2 -1- x – a? d lim x→0

A:

Q: lim х>1 \x-1 X→1 Inx,

A:

Q: lim 0 3x²+5 cos x- 2x -5

A:

Q: 2x lim x→0 Vx + 1 – 1

A: Given limit expression is limx→02xx+1-1.

Q: Q.1 Evaluate the limit x-3 sin2x 1) lim(2x2 +x + 1) 2) lim 2-9 3) lim x-1 x-3 x2-x+1 4) lim x+00…

A: We have to find limit

Q: 2x -cos(2x)- 2x - (b) lim | x2

A:

Q: f (x+h)- f(x) 7x3-2x-1 Using lim-0 Find the slope of the tangent line y 5x+2 h at x = -1.

A:

Q: x2-4 1) lim x-2 x-2 sin 2x 2) lim 1 1 3) lim(-- X-0 x VX

A:

Q: 3/x – 3 (k) limx→-∞ 5 - x x³ +1 (1) limx→-∞ Cos -0- x6 +x5 + 100

A: For (k), We need to find limx→ -∞ x-35-x3. So,            limx→ -∞ x-35-x3We know that,…

Q: 12. lim(-x + 5x – 2) 14. lim (x – 2x² + 4x + 8) - X→-2 16. lim (8 – 3s)(2s – 1) s2/3 -

A:

Q: 2. lim V2x+1-V3 ズ→1 ズー1 0.9 0.99 0.999 1.001 1.01 1.1 f(x) V2x +1-V3 : lim ズ→1 x-1

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: 1-x c) lim- x1 1-Vx こ 11- sin x d) lim エー→0

A:

Q: Inx lim X+o x3 lim- x-0 ex - x2 - 1 lim- 0 sin'3x

A:

Q: sin(2Tx) lim x → 3 x2 – 9 | O -0.6667 T O 0.6667 T O 0.3333 ↑ О -0.3333 п

A:

Q: x2-x-2 2x-4 2sin(6x–12) 3(x-2) Sx-1 Let f(x)* ,g(x) • and h(x) Vz+2+1 a. Find lim f(x), lim g(x),…

A:

Q: 1. lim x²-1 al 2. Tく-X b) lim X-Sin 2x +3 c) lim Vey?-x

A: Given- limx→1x2-1x10-1

Q: 3) lim Lnx .tanx x-0+

A: Use lim sinx/x and L'Hospital law .

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: x+6 lim x--6t x+ 6 lim x6 x6 Jx 6 lim x6 x6 =

A: If x-> -6^+ then x>-6That means x+6>0So, |x+6|=x+6Answer(a): limit x-> -6^+ |x+6|/(x+6)=…

Q: lim 4y° + Jy18 – 1 -00

A: Given that: limy→-∞4y9+y18-1

Q: lim -Vx + +sin(x)cos(x) 1+In (x)

A: Topic:- limits

Q: 1-sinx x²-49 b. lim x→7 x-7 lim C. lim X→00 x²+1 a. X 1-cosx

A:

Q: 13. lim f(x), where Sx+2 xS2 3x-5 x> 2 f(x) = 14. lim f(x), where Sx* - x +1 x 3

A:

Q: 11. lim x→ー4 x2-16 2x2+9x+4 z2-36 12. lim Z--16 Z-6

A: (a) We have the given limit problem as limx→-4x2-162x2+9x+4 On calculating the factors of numerator…

Q: (2-4)² limx-1 sin(x3-1) x-1

A: by using limit algebra and L' hospital rule

Q: 4-V16+h 9. lim x+sin x 12. lim

A: Note: As per bartleby guidelines for more than one questions asked only one question is to be…

Q: 18. L6. 4- x² lim lim x² + 3 x→2 3- vx²+5 lim (2x x →2 x →0 21. 19. 20. lim v25 – x2 lim 12 sin (÷)…

A: We have to find out limit

Q: 2Tan 'x - x 9. lim,0 'x0 2x – Sin 'x

A:

Q: -11x lim I+00 11 + 2x -1 6x – 12 lim 1-00 r3 + 9x – 14 ,2 lim x→0 12 – 15x? V2² + 15x lim 5х — 13…

A:

Q: Q4:Evaluate 1) lim (1-1) x-0 \sin x

A:

Q: 3 lim tan³ 2x x→0

A:

Q: 2x + Vx x² + 4x 3 1. lim 2. lim 7x2 + 2 sin x 3. lim x→-o x + e* 4. lim et 2xe2x In x 6. lim 5. lim…

A: To decide whether the given limit produces an indeterminate form6. limx→∞lnxx

Q: 3 limy 0 1 - x!

A: This is the problem of limit and calculus.

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

A:

Q: 1f. lim (tanx)x x->0+

A: Given,

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

A: (a) We take L.C.M. in the numerator and cancel the common terms in numerator and denominator. Then…

Q: (1) lim t2 (2) lim x0 Vx2 +3 2x + 1 -1 x00 7 - t2 x2 1 (4) lim 3t2 n2 (6) lim x0 Vn3 + 2n 5t (3) lim…

A:

Q: V+12-4 3 .lim X-2 tan3x 2. lim X-0 sinax 4). lim X00 x-7x+1 x-2

A:

Q: lim COS X tanx メー→o <-2メ4リX-8 2lim 3 メ→ 2 xリ_2X メ-2 xツ_2Xメ

A:

Q: 2x (1) lim x→0 3– vx+ 9 -

A:

Q: Q2) Find : (a) lim (2 + x) x-4+ 16-x 1-secx 0 sinx cos2x sintx (b) lim (c) lim (d) lim x-0 sin2x…

A: Dear student, According to bartleby guidelines when student post more than one question then expert…

Q: х — 1 lim x→1+ Vx + 2

A: Here we need to find the right hand limit only.To find the required limit substitute the variable…

Q: -2x - 4 f) lim x--2 x + 2x ut | g) lim u-1 u3 1 4х — х2 h) lim x-4 2 - Vx Ya

A: As per our guideline we are supposed to answer only first three subparts. Kindly repost other parts.…

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.