b): Evaluate each of the following limits: 1- cos* 3x 1)lim 9x2 x sin 5 12)lim r+00 xt + 1

Q: Compute the following limits if they exist. sec r – 1 (a) lim z-40- 23 I – sin r (b) lim 1+0 x - tan…

A: L. Hospital RuleIf limx→a f(x)g(x) = 00 or v6c6 formThen differentiate f(x) & g(x) and take…

Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

A: Given :limx→01-cos4(x)sin(2x)lim x→1 lnxx2-1lim x→π4 sinx-22cosx-22lim x→01+tan(2x)1x

Q: sin 7x lim x→0 sin 3x

A: The given limit is limx→0sin7xsin3x

Q: cos 3x-1 1. lim 1 L2

A:

Q: Find the following limits if they exist. 1 lim 1 a) b) sin x-1 lim cos x

A:

Q: b. Evaluate the following limits: lim 7* cos)-7x – lim 5x2 COS [sin(-2x)sin(5x)sin(7x)] 2x*cos(x)

A: Rewrite the expression as:

Q: Which of the following limits is in an indeterminate form? Select all that apply. sin x lim х—1 х —…

A:

Q: 1. Determine whether or not each of the following limits exists as a real number or as +oo or -oo.…

A: According to the given information it is needed to check whether the limit of the following…

Q: 7. lim x* sin 4 x>0

A:

Q: Evaluate the limit, if it exists. If not, determine whether the one-sided limits exist (finite or…

A: If on substituting , we get 0/0 form, we use L - Hospital s rule, where we need to differentiate…

Q: . Evaluate the following limits if it exists. If not, explain. sin(90) lim 0-0 %3D 40 4

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Hence, determine whether the function is continuous at x = 2x. ) Find the value of k such that the 5…

A:

Q: 1. Evaluate the following limits. - 2 lim a.+2 -4 V2 +1-2 lim b. i+2 t-2 | sin 7r lim c.0 sin 3r

A: As per as our guideline i am supposed to solve only 3 part of question 1 . And f getting solution of…

Q: Evaluate the following limits tan x – sin x sin(x – 2) (a) lim x→0 x(-1+ cos³ 2x) (b) lim x→2 Vx + 3…

A:

Q: We can use direct substitution in computing limits provided there is nodivision by zero, which is…

A:

Q: Compute the following limits if they exist. x - sin a tan x (a) lim 10+ Vr (b) lim (c) lim tan r -…

A:

Q: Calculate the following limit: 131). lim(1x)ª sin(5). 13л x→0

A:

Q: 4. lim ¹-cos 2x x-0 sin 2x

A:

Q: find the limit or explain why it does not exist. cos 2r – 1 lim sin x

A:

Q: Find the value of each limit: 1- cos x а. lim x→0 x+x b. lim sin(x+ h) – sin(x) h h→0

A:

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: Find the limits in Exercis

A: Given: L=limx→0x-xcosxsin23x

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

A: limx→0cos2x-1sinx

Q: Evaluate the following limits: 1. 2 sin x - sin(2x) -x-sin x (a) lim 25 -t2 (b) lim 15 tl 11m,…

A: Hi, since there are multiple sub-parts in the questions posted, we will answer first three subparts.…

Q: I. Evaluate the following limits. 1 1 1. lim x – 1 et — е x→1+ - - tan x 2. lim (sin x x→0+

A:

Q: B. Evaluate only three of the following limits tan 30 lim 0-0 sin 80 x+1 i. ii. lim + zX co-x 1 = 2…

A:

Q: lim = 0 sin x.

A: limx→01x-1sinx=0

Q: Evaluate the following limits: 1 1 (i) lim{ sin -+cos- X X 1/x 1/x +a, 1/x a1 + (ii) lim ..... ,a1…

A:

Q: Evaluate the limits sin3h-2h 4) lim sin?x 5) lim x 0 1-cos x

A: (4) limh→0sin3h-2hh=sin3(0)-2(0)0=00=indeterminate form Apply L'Hospital rule,…

Q: lim sin?(2 – x) cot²(x² – x – 2) - X→2

A: We have to evaluate the limit at x= 2.

Q: (a) Evaluate two of the following limits: 1-cos ax sin( 1-x² ) tan 2x (i) lim x→0 1-cos bx (ii) lim…

A:

Q: Q3: Find the following limits if exist:- 1-cos 2x (1) limx-0 sin² x

A: If it is required to evaluate the limit limx→af(x)g(x)=00. That is if applying the limit leads to…

Q: Determine the following limit: 17x sin(17x) - lim x →0 17x – tan(17x) -

A:

Q: Compute the indicated limits. sin(2x) lim 3x

A:

Q: . Evaluate the following limits. 1.lim cos .2 () 2. lim sin x→0 (- 3. lim 3¬× X→-2

A: 1. limx→πcosx22. limx→0sinxx3. limx→-23-x

Q: Find the following limits: cos( TX) 5. lim 2-x 3x 6. lim tan 1+x V4x²-5 lim 7. x+2

A:

Q: Solve the following limits. (a) lim r In x (b) lim 2+ sec (3x) (c) lim 7/6 tan (3I) –1

A:

Q: B) Evaluate two of the following limits 2) lim(cos² x – sin² x) - 8

A:

Q: lim (sec'x - tan'x) = ∞ tan’ x) = 0

A: To show indeterminate of limx→12π(sec3x-tan3x)=∞

Q: I. Evaluate the following limits. 1 1 1. lim x – 1 et — е x→1+ - - 2. lim (sin x)tan a x→0+

A:

Q: 4. State and prove the law of sines in triangles. 5. Prove lim,0 V2r + %3D 6. Figure out the…

A:

Q: 1.a) Evaluate the following limit using the Squeeze Theorem limx→∞  sin(x)/x b)Evaluate the…

A: We have to find given limit with the help of Squeeze Theorem.

Q: sin4x' limx-0

A:

Q: Evaluate the following limits if they exist. 1 — х — е" a) lim 2(1 — е") b) lim (1 + sin x)'/= sec x…

A:

Q: Find the limit. 2x2 3. lim Cos

A:

Q: Find the limit. lim tan(9t) t→0 sin(3t)

A: before we solve the following question we need to know the limit of the trigonometry function which…

Q: Evaluate the limit. 3 sin? 2x lim х—0 8x2

A:

Q: Evaluate using Theorem 2 as necessary.

A: Given: limx→0 x2sin2(x)

Q: 1-28, evaluate the indicated limit, if it exists. Assume sin x that lim L I sinx 1-0 tan x 9. lim

A: We need to evaluate the following limit if exists.

Q: () 2. Use the Squeeze Theorem to evaluate lim r COS

A: Given problem:-

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.