Find the limits in Exercises 25–30. sin (1 – cos x) х sin x 25. lim x→0 26. lim x-0" sinVx sin (x² + x) sin (sinx) 27. lim x→0 28. lim х sin ( Vx – 3) sin (x² – 4) 29. lim 30. lim x→9 х — 9

Q: Evaluate the limits in Exercise 7 and 8. 7. lim sin t dt 8. lim x cos t dt

A: (7) ∫-xx sin t dt =-cos t-xx=-cos(x)--cos-x=-cos(x)--cosx=-cos x+cos x=0 So we get limx→∞ ∫-xx sin…

Q: Q3: A) Find the limits below 1) lim (x,y)—(0,0) x² + sin²y 2x2 + + y²

A:

Q: By considering different paths of approach, show that the limit xY COS Y lim does not exist.…

A:

Q: Calculate the limits given below In(In x) (sin x)2 a) lim In x b) lim(x + sin x)tan x c) lim х-0+…

A: Part a,Given,         limx→∞lnlnxlnx

Q: 2) By using E-S definition of limit, show lim (x+y+xy)cos÷ cos 음-0 COS (xy)(0,0)

A: Let f(x)=x+y+xy cos1x cos1y

Q: Find the value of the limit lim SINX X 0 2x 02x (a) 0 (b) 1 (c) 1/3 (d) 1/2 (e) 1/4

A: Here we have to find the limit of the function. In the first step use the property of the limit:

Q: Use l’Hôpital’s rule to find the limits in Exercises . x² . 8. lim x--5 x + 5 х — 2 7. lim x→2x2 25…

A: We’ll answer the 7th question since we answer only one question at a time. Please submit a new…

Q: 2] Show that the limit does not exist by considering the limits as (x, y) → (0, 0) along the…

A:

Q: 2. Use a table of function values to estimate lim in3x sin 3x sin3x -0.1 0.1 -0.01 b. 0.01 -0.001 c.…

A:

Q: 1. Determine if the following limits exist: x² + y5 lim (x,y) (0,0) 1 - cos(x) + y4 (a)

A: Sol: Part (a) limx, y→0, 0x2+y51-cosx+y4Find two different paths to approach the point that gives…

Q: Use the two-path test to prove that the following limit does not exist. x+ 2y lim (x.y)→(0,0) *- 2y…

A:

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x→0 sin 2x

A: Here we will find out the required value.

Q: Evaluate the following limits (if exist): 1-cos(ax) (c) lim- a+0 (d) lim/Vxr'+x-Vx°-cx), where c is…

A: To evaluate the given limit we are using L- Hospital rule

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(7/2)-(tan x)" (2) limy-o…

A:

Q: Estimate the limit numerically or state that the limit doesn't exist lim h→0 cos(9/h)

A: We will pick some values for x. Then we will find values of y for those xs.

Q: Q1: Find the Limits of: Тan x 1- lim X+Sin x+VX 2- lim xo X+Sin x 3- lim vx2 + 1- Vx2-x

A:

Q: The value of limit x→0 of {sin (a + x) – sin (a – x)}/x is

A: we have to find the value of  limx→0sin(a+x)-sin(a-x)x

Q: Evaluate the limits in Exercise 7 and 8. cos t dt sin 8. lim x x→0+ 7. lim

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the limits in Exercise

A: Given,

Q: Find the value of the following limits: 5y 1-limy→o tan 10y 2-limx-0 6x cot3x 7x²+8x 3-limx-0 4x²…

A:

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x

A:

Q: Find the limit. lim (cos(t), cos(t), t In(t)) t-0+

A: Given: limt→0+cost, cost, t5lnt

Q: is lim x = inf (xn) as x, y. What Express answer and = 3n lim sup (xn) where Xn = [(-1)³ ]+2?

A:

Q: Find the limit. lim (cos(t), cos(t), t* In(t)) t-0+

A:

Q: Find the limits in Exercises

A: Given: limx→∞x57+x-3x57+cos x   ……1

Q: Find the limits in Exercise

A: Given: limθ→π4tanθ-1θ-π4

Q: Evoluate the limit of (1-cosx) (x²) as x pproaches 0.

A:

Q: Find lim(r,y)→(0,0) ry" Cos y if it exists or show that the limit does not exist:

A: Solution :-

Q: Find the limits in Exercise

A: To find the limit  limθ → π6 sin θ - 12θ - π6

Q: Find the limits. Enter "DNE" if the limit does not exist. lim cos (x.y)¬(0,0) x' – y' x² + y² 4x lim…

A: Find the limits : Given :            lim(x,y)→(0,0)cosx7-y7x2+y2               =  cos 0-00+0…

Q: Evaluate the limit sin(a – Vy) lim (2,y)→(1,1) x - y

A: Here, we will use the following formulas,

Q: 6. Figure out the following limits without applying L'Hopital Rule. sin(r- 4) V2r -1-1 b. lim (2²…

A:

Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x A) 3 B) 0 C) D) Does not exist 4/5 -/2

A:

Q: X,xif limF,(t)= F(t) at all t for which Fis Continuous

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the limits in Exercises 9–12. sin 2x cos 0 9. lim 10. lim 0→- 30 х r + sin r 2r + 7 – 5 sin r 2…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: (a) Compute the following limits: (i) lim **+x²+x+1 x2-1 sec-1(vZ+h)-sec-1/2 (ii) lim h→0 h

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(n/2)-(tan x)cosx (2) lim,--0…

A: L'Hôpital's rule states that for functions fx and gx which are differentiable on an open interval I…

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

Q: Prove that lim vx sin (2) = 0 using the Squeeze Theorem. x-0+

A:

Q: Find the limit and discuss the continuity of the function. lim sin 1. (K. y)(27, 4) y lim 2. (x,…

A:

Q: Find lim r(t) when 5 In t r(t) = (: 2 tan¬lt, e-2 t 2 tan-t, e 1. limit = (2т, —2, 0)

A: Given    r(t) = 2tan-1t , e-2t , 5 lnttwe need to  find  the limt→∞ r(t)=?

Q: a)Express the limit as a definite integral. Σ (3c-5)Ax, xe[0,1] lim 2 b) and then evaluate it.

A: lim∆→0∑i=1n3c2i-5∆xi  x∈[0,1]∑ =∫∆xi=dx∫01(3x2-5)dxThis is definite integral

Q: Find the limit or prove that it does not exist lim (2,y)→(0,0) T° cos x + 2y sin y x2 + 4y2

A: We will evaluate the limit limx, y→0, 0x3cos x+2y3sin yx2+4y2  using polar coordinates.

Q: Calculate the limit limx→0cos(x+a)−cos(x−a)x

A: We have to find the limit: limx→0 cosx+a-cosx-ax This is simple limit so putting x=0 in the…

Q: - Find the limits using L-Hopital's Rule: cos 3x 1 (а). im $ x→0 X* (b). lim (e - 1)*

A:

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x A 1.

A:

Q: Find the limit: lim f(x) as x approaches 0 of Kx2 - tan2 (mx)cos(mx)/x2     (m not =0)

A: Consider

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim 0 sin 2 -16 2. lim 4 (V+5)-3

A: 1. Here limx→07xsin 2x is of 00 form, so by applying L. hospital rule, we get limx→07xsin 2x =…

Q: 2. Find the limit using Squeeze theorem 1 lim,2|a – 2| sin( `x – 2

A: Given: limx→2x-2sin1x-2

Q: (b) Use the sandwich theorem to show that limy0x°cos - = 0. 1 In order to apply the sandwich…

A: