O Determine the following limits O limx-0 3 1+y3x+1 sin 2x limx-0 10x"+x*+31 limx-too

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: 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: b. Evaluate the following limits: 7x cos)-7x lim- [sin(-2x)sin(5x)sin(7x)] lim 5x2 2x cos(x) X-0

A: We write the given limit in the following format

Q: Evaluate the following limit. limx→0 tan(3x)/sin(2x)

A: Evaluate the limit

Q: Compute this limit to infinity, no lhoptials rule   limx→∞ of x−sqrt(2x^2+ 1).

A: We have given limx→∞ of x−sqrt(2x^2+ 1).

Q: Find the following limits: a) lim (1 + 3x) lim[x- In(x+1)] b) sin 2x lim x0+ 5x d)- lim sec hx e)…

A:

Q: Evaluate the limit lim (sin(4x + 5) + 5) - I 00

A:

Q: х — 1 X - 1. lim ( 1 2x – 1 |4x² – 1| x→2

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Evaluate the following limits: 8x3+27 lim- 4x2+12x+9 X -- 2 b.) lim (3x + v9x2 — 6х + 3) X -00 c.)…

A:

Q: Evaluate the following limits: (a) limx→0 4x/sin 5x (b) limx→π sin( π/2)/5x (c) limx→0…

A: a) limx→04xsin(5x)=45 b) limx→πsinπ25x =sinπ2limx→π15x                    = 015π limx→πsinπ25x = 0…

Q: x2 + 8x – 9 4. lim x→1 x3 2а? — 5х + 6 - -

A:

Q: Find the following limit.   Lim  x→0+          ( 2x sec( 3 π/2 - x))

A:

Q: Evaluate the limit: lim z-10 sin (4z)

A:

Q: Compute the following limits and write your answer to the boxes. lim 2x cot lx %3D 7x2 lim x2 28x -…

A:

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:

Q: Find the following limits.  limx->+infinity (sin2x)/(x2+1) limx->+infinity (e-2x cosx)…

A:

Q: 2x + 1 (a) lim 9x2+ x

A: We have to solve the limit

Q: Exaluate the following limi- 1. lim to + x' xー>-○ x(- 2x2 +5) x° 2. lim sin 3(2x+1) ×ー>-ム 2 2x +1

A:

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: 2. Calculate the following limits. Justify your answer. (without using L'Hopital's rule Rule or…

A:

Q: 5. Use the definition of limit to prove that lim[(x – 1)(sin x²)] = 0

A:

Q: Evaluate the limit: lim sin(7x) cos(4x)

A:

Q: swer of the following lim 2x²+6y² lim (x,y)→(0,0) x²+y²

A:

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: Find the limit: lim cos(5log6(7^x)) x-> negative infinity

A:

Q: Q. Prove that: Lim tanhx =1 .

A:

Q: Q3. Compute the following limits if they exist. SEC x – 1 (а) lim x→0- sin x (b) lim x→0 x tan x 2 -…

A:

Q: Q4: - Evaluate the limit of the following: x3–1 sin 2x 1-V 1) lim 2) lim x→0 2x²+x 3) lim x→1 1-x…

A: When we get 00form, we can us  L' Hospitals Rule to calculate the limits. In this rule μx→a…

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

A:

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: tan 0 1) lim 0-0 02 cot 30 -x* 2) lim x00 x-7 x3+7x²+1 x+3 3) lim x-3…

A: (1) The given limit is: limθ→0tanθθ2cot3θ=limθ→0sinθcosθθ2cos3θsin3θ=limθ→0sinθsin3θθ2cosθcos3θ It…

Q: 6 Compule the following limit lim glx) whene X-0 9 = (05 (2x) x९ o ( ৪-४, ४>0 where

A:

Q: use L'Hôpital's Rule to compute the limits: (1++)" (а) lim 2x. (b) lim (x tan r. 2.

A:

Q: Evaluate the limit tan 5z lim I0 sin 2z

A:

Q: does this limit exist! lim X-7+00 X(zt sin 7x) x+1

A:

Q: Evaluate the following limits: x + sinx lim х-оо 2х + 5 lim - х-0 tan3x 1- Vx lim x-1 1 - xX x. Sinx…

A:

Q: Evaluate the following limit or explain why it does not exist. limx→0 (x[1 − 2x − cos(2x)])/((x −…

A:

Q: lim-0 OI Oll O III OIV e² - x Not Indeterminate کے

A:

Q: Calculate the following limits, or explain why they diverge. x2 – 9 lim 1--3 x+3 lim 2x + sin 3x

A:

Q: Evaluate the limit, using L'HÔpital's Rule if necessary. sin 3x 1. lim x→0 tan 8x In x5 2. lim x7 –…

A:

Q: 12 Show that the following limits do not exist. 1 lim X0x (a) (x > 0), 4,

A:

Q: Evaluate the following limits using L'Hopital's Rule when possible. a) lim,- (2) b) lim (1+ æ) +0+

A:

Q: Evaluate the following limit; using L'Hospital's rule if possible: limx→0 (2x+tan(3x))/(4x−tan(5x))

A: Given integral is When x=0 Therefore, given limit is of indeterminate form (0/0).

Q: find the following limits if exist:- limx-0 1-cosx x sinx

A:

Q: Evaluate the following limits: x – 25 (i) lim x+25 Vx – 5 Vx² – 3 (iii) lim x→-o 4x +5 sin(50) х — 3…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find the following limit: 3. 1) lim (1--) x00 2) lim (Lnx) 3) lim (x² – 1)cos* X-1

A:

Q: Use l'Hôpital's Rule to find the following limit. 5 sin (x) - 5x lim 2x3

A:

Q: 1. Find the following limits: sin x a) lim- b) limxe*

A: Solve limit as general

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.