Find the limitssin(3t)limIn(sin(3t))j+tln(3t) kLi+t+0 sin(t)In(tan(t))t3 – 27limt2 – 4t + 3i+t2 – 2t – 3j- (t – 3) In(t – 3) k =t→3t – 3

Since you have asked multiple questions in a single request so we will be answering only first…

Answered: Find the limits [ sin(3t) lim Li+…

Math

Calculus

Find the limits [ sin(3t) lim Li+ In(sin(3t)) j+tln(3t) k sin(t) In(tan(t)) t+0

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: sin t lim + 2 t+0 t

Q: Find the limit, if it exists.

A: The limit of a function limx→Xfx=Y means that value of function f(x) can be as close to Y by making…

Q: 9. Evaluate the limit. lim (1+ sin 3x)1/x x→0+

Q: Find the limits sin(3t) lim In(sin(3t)) -j+tln(3t) k| = -i+ t+0 [ sin(t) In(tan(t)) t3 – 27 i+ t – 3…

A: We need to find the limit.

Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x 4 A) 을 B) 0 530 C) D) Does not exist

Q: Q3 :(A): By using "L' Hopital rules"; Find the limits of : 1 (1) lim,-ol1-cos x sin2x (2) lim,…

A: 3)1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0(tan-1x-x) /x3 Repost the next question.

Q: Find the limit. cos(x) – 1 +x2 lim x-0 2x4

A: It is given that, limx→0cosx-1+12x22x4.

Q: Find the limit. lim (1+ sin(3x))/* x→0+

A: Given: u=(1+sin(3x))1x We want to find limx→0+u=limx→0+(1+sin(3x))1x Since we know that u=eln(u)…

Q: lim 4 sin(x + n) + 3

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

A: 3 1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0 (tan-1x-x) x-3

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

Q: Evaluate the limit. –1+}² 1.2 COS I lim 2.x4

Q: Find the limit. t2 j+ sin(7t) k sin2(t) -2t ¡ + lim t→0 e

A: We have to find the limit: limt→0e-2t i+t2sin2t j+sin(7t) k

Q: Find the limit of the trigonometric function .

A: The given limit limx→0cosx-sinx-12x can be evaluated as, limx→0cosx-sinx-12x=cos0-sin0-12×0…

Q: Find the limit. lim sin-12r i ||

Q: 2. Find the the limit. li -y 1 (tany): 2 Y- 2

A: Given that: limy→π2-(tan y)π2-y

Q: Find the limits in Exercise

A: Given,

Q: Pr. #3) Prove that the limit does not exist. cos(4ry)- 1 lim (x.v)-(0,0) 2r + 3y4

Q: Find the limits lim x→ -1+ cos-1x

A: We find the limit by substitution

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

A: Given: limt→0+cost, cost, t5lnt

Q: what is the limit of (cos(x))^4/x^2 as x approaches 0 from the positive side?

A: Given,

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

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

Q: compure the limit ) um X-7-3 X3-9x 6+2X Sin/2x) 2) lim sini2x) X-7ut x2 3 X 3) lim X-7-00 イ4メ2tメt5

A: Given: -

Q: Find the limit or prove that the limit does not exist. lim_(x→0) sin(1/x)cos(1/x)

A: In the given problem we have to find the limit of prove that the limit does not exist.…

Q: Find the two limits: sin 2x lim r-T/2 COS x

Q: 8) Find the limit (exact value) a) lim Vy - 3y – y ytoo tan ax b) lim- x→0 sin bx (a ±0,b± 0)

Q: 5 sin(2z) z-40 1- cos(2) Find the limit. lim COS

Q: )Use the Sandwich Theorem to show that lim cos x-1 =0. x2 Find f'(x) for f(x) = sec(vx2 + 1).

Q: Q2.) Find the limit ( 1 lim X+x cos x 1. X→ 0 sin x cos x |x + 2| 2 - lim(x + 3) x-2 x + 2 lim sin…

A: solve using properties of limits

Q: Evaluate the limit. lim (sin(4t)i + cos(5t)j + tan(2t)k)

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

Q: Prove rigorously that lim sin 1/x does not exist. x → 0

A: Let the given limit be y - y = limx→0 sin1xy = limx→0 sin1x1x×1xy = limx→0 sin1x1x×limx→0 1xy =…

Q: Find the limit of tan^-1(e^(x^2)+x^2+1/x) as x approaches negative infinity

Q: - Evaluate the limit a-Lim(x/(x-1) – 1/ Inx) b- lim [In(cos(x)) c-2-VX-+4 /sin'x x>1 x>0 d- lim x+1…

A: Limit values

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

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

Q: Find lim 2x sin using the Squeeze theorem. x-0

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: f(x) lim sin(5x) X I 0 -0.25 3 2 Estimate the limit numerically or state that the limit does not…

A: We have to find out limit

Q: Find the limit: 1 – cos(x) lim x2

Q: Find the limits: x² – x - а. lim x→1 In x e* – 1 b. lim x→0 sin x .3 c. lim С.

A: Limits using L'Hospital Rule

Q: Find the limit. lim sin-2x i

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

A: Consider

Q: Find the limit. lim X→- 47 Vx+ 15 cos (x+ 4x)

Q: 2. Evaluate the limits numerically. x-1 a) lim x-1 vx+3-2 x² +3x+2 b) lim x--1 x2-x-2 cos(x)-1 c)…

Q: Q2.) Find the limit ( 10 lim 1- X- 0 X+ x cos x sin x cos x |x + 2| 2 - lim(x + 3) x-2 x + 2 lim sin…

Q: Find the limit. cos(x) – 1 +x² .2 lim 2x4

A: NOTE: Refresh your page if you can't see any equations. . apply L'Hopital's rule

Q: Find the limit. tan(12t) lim t-0 sin(4t)

Q: Compute the following limits if they exist. sec r - 1 (a) lim I0- r3 x – sin x (b) lim I0 x - tanr 2…

A: We are entitled to solve 3 subparts of first question so, I am providing you the solution of the…

Concept explainers

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.

Question

Find the limits
sin(3t)
lim
In(sin(3t))
j+tln(3t) k
Li+
t+0 sin(t)
In(tan(t))
t3 – 27
lim
t2 – 4t + 3
i+
t2 – 2t – 3
j- (t – 3) In(t – 3) k =
t→3
t – 3

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Limits and Continuity$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

(a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t. Then (b) evaluate dw/ dt at the given value of t. 1.w = 2yex - ln z, x = ln (t2 + 1), y = tan-1 t, z = et ; t = 1 2. w = z - sin xy, x = t, y = ln t, z = et-1 ; t =1
(a) express ux, u y, and uz as func-tions of x, y, and z both by using the Chain Rule and by expressing u directly in terms of x, y, and z before differentiating. Then (b) evaluate ux, u y, and uz at the given point (x, y, z). u = e^(qr) sin-1 p, p = sin x, q = z^2 ln y, r = 1/z; (x, y, z) = (pai/4, 1/2, -1/2)
Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).
Determine the 1st and 2nd degree Taylor polynomials L(x,y) and Q(x,y) forf(x, y) = tan−1 (x + 2y) for (x,y) near the point (1,0).
Find T4(x) Taylor polynomial of degree 5 of the function f(x)=cos(x^3) at a=0
4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard theorem for a suitable domain D. b. Then estimate the interval of existence of the solution.
(a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t and differentiatingdirectly with respect to t. Then (b) evaluate dw/ dt at the given valueof t. w = 2yex - ln z, x = ln (t2 + 1), y = tan-1 t, z = et ; t = 1
f 1 (x) = x and f2 (x) = sin (x) sin Wronskian functions that are linearly independent show using.
(a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t. Then (b) evaluate dw/ dt at the given value of t. 1. w = x2 + y2, x = cos t + sin t, y = cos t - sin t; t=0 2. w = x/ z + y /z , x = cos^2 t, y = sin2 t, z = 1/t ; t =3
Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t.
Use field II to sketch the graphs of the solutions that satisfythe given initial conditions. a) y(0) = 1 b) y(0) = 2 c)y(0) = -1
4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard theorem for a suitable domain D. b. Then estimate the interval of existence of the solution. Use applied analysis and then I want the solution handwritten.