i. lim -cosx) j. lim sin x

Q: What is lim x=inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^(3n)] + 2? (express answer as x,y)

A: Solve the following

Q: What is lim Sináx, cosx А. 0 В. 6 С. 1 D. Ø (DNE) Ø (DNE)

A:

Q: Use l’Hôpital’s rule to find the limits

A:

Q: Evaluate: lim (sec z sin z)ot z

A: Note: We are entitles to solve only the first question, unless specified To evaluate :limx→0(sec x…

Q: Evaluate using Theorem as necessary.

A: Given : The limit is limt→0 sin2tt .

Q: Find the limits in Exercis

A: Find the limit: limθ→0sinθsin2θ Solution: We know that, sin2θ=2sinθ cosθ Evaluating the limit.…

Q: What is lim m→0 sin(m) m ?

A:

Q: Evaluate using Theorem as necessary.

A: Given limit: limt→0 t3+9sin tt We can write the above limit as limt→0 t3+9sin tt=limt→0 t3+9×limt→0…

Q: Find tant r lim t

A:

Q: Find the limit. y sin x limx.y)(0,1) O 1 8. O No Limit

A: Find the limit. lim (x.y)→(0,1) (y5 sin x)/x To select correct option  1 0 ∞ No Limit

Q: find the limit or explain why it does not exist.

A: We have to find the limit: limx→π cos x2+sin x This is determinate form of limit so we need to put…

Q: Use l’Hôpital’s rule to find the limits

A: The L’Hospitals rule is used to obtain limits of a function when it occurs in the indeterminate form…

Q: Find the limit of the trigonometric function.

A: Given: limx→π2sin x To Find: The limit of the given trigonometric function

Q: Evaluate the following limits. 2x sin- x 1. lim х-0 еx — х — 1 2. lim (sec x)cot × X-

A:

Q: Show that lim (2,v)>(0,0) **+y D0.

A:

Q: True or false: lim(sin) as x goes to infinity exists.

A: Given, limx→∞sinx Find in the following that this limit is exist or not.

Q: Use the Squeeze Theorem to evaluate lim sin(ln x) csch(cot x). x→0+

A: Given:                                                                fx:=sinlnxcschcotx. To do:…

Q: Use l’Hôpital’s Rule to find the limits

A: Given: limx→π2-sec7xcos3x we know that  secθ=1cosθ so, limx→π2-cos3xcos7x  00 form it is 00 form, so…

Q: If a > 0, show that sin(nx) lim d.x 0. n→∞ nx

A: Solution

Q: Find the limits in Exercis

A: Given: L=limx→0x-xcosxsin23x

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

A:

Q: lim sin (2 – t) cot (t – t – 2) t+2

A: Given that: limt→2sin2(2-t)cot2(t2-t-2)

Q: Use the Squeeze Theorem to evaluate lim sin(tan r) sech(secr). ес

A:

Q: (c) Prove the value of lim Sin 3a o Cos 4Do NOT use L'Hospital's Rule.

A: The given limit is,

Q: Find the limits. Are the functions continuous at the point being approached?

A: Given function is  Since, the function f(t) exists finitely at t=0, so we will evaluate the limit…

Q: - lim a sin

A: We have to find limit using l'Hospital Rule

Q: lim (sin r)tan z T/2

A: Given problem :- Identify the indeterminate form and evaluate limx→π-2sinxtanx

Q: ■ Find the limit.

A: Here limx→∞sin2xx2=limx→∞sinx2x2.

Q: (a) Show that tan x = sec?x using quotient rule. dx x+8 (b) Find lim X-2 x+2

A: Solution-

Q: Find the limit of the trigonometric function.

A: Given:limx→0 sec2x

Q: Use l’Hôpital’s Rule to find the limits

A: We have to find the limits by using L 'Hospital's rule: limx→0sin mxsin nx In L' Hospital's rule we…

Q: Find the Oimits :- sin 3y Lim Sin Jz8 Lim My JzO ot

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Clearly explain why lim (sin-(t) is equal to 1 and not zero. t+0+

A:

Q: Find the limits

A: We first try to find the limit by substitution

Q: What is the lim, 0+ sin(y) In(y)?

A: limy→ 0+sinylny=limy→ 0+lny1sinyBy L'Hopital's rule,=limy→ 0+1y-cotycscy=limy→…

Q: E. Use L'Hopitals's rule to find lim (2 – r)tan(r=/2).

A: Topic = limits

Q: IV. Do as indicated. Use Squeeze Theorem to evaluate lim sin(sinh x) csch z.

A:

Q: Use l’Hôpital’s rule to find the limits

A:

Q: ах Determine the values of a and b such that lim Vax +b – 3 = 5. x→0 bx

A:

Q: Evaluate limt-->0(tan 4t)/(t sec t) Without using L'Hospital's rule.

A: To calculate the required limit without using the indeterminate form

Q: How do you solve the limit of this graph?

A: x->-1^- means x is slightly less than -1.

Q: Lim 1 Sin?x

A: Calculate : limx→01sin2x-1x2

Q: lim zsin lim z*. lim sin 1

A:

Q: is lim (sec x)ot æ 2

A: Apply exponent rule

Q: Lim sin x X0 Cos 2x -cosX

A:

Q: Evaluate the limid lim X'sin t X→o sin x?

A: We have to find limit

Q: Sinx +x 3) lim tan x

A: Given limit is : limx→0sinx+xtanx Use property of limit  limx→0sinxx=1limx→0tanxx=1

Q: lim sin (2 – t) cot? (² – t – 2) t+2

A:

Q: Use the Squeeze Theorem to evaluate: lim x→0+ sin(ln x) csch(cot x).

A: Solution is here

Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

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.