22. Evaluate the following limits : x + Sinx 1+ Sinx a) lim b) lim 2x + 5

Q: sin 7x lim x→0 sin 3x

A: The given limit is limx→0sin7xsin3x

Q: Prove the limit statements lim x sin = 0 y=x sin 2

A: Prove the limit statements     limx→0x sin1x=0

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

A: Evaluate the limit

Q: Find the limits in Exercis

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

Q: Evaluate the following limits. 1. lim 1 cosh x x+0+ ln(x² + 1) 2. lim (tanx) (sin x-1) x+7+

A: Let's solve for given limit.

Q: Compute the following limits if they exist. sec r – 1 (а) lim x – sin x (b) lim T→0 x – tan x 2 – VE…

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

Q: lim x →3 2+e* sin(7x)+x+1

A:

Q: Find the limits in Exercise

A: Limits are used to calculate the approaching value of the function at which the exact value of the…

Q: Question 3 limx→+∞ e-√√ OI Oll O III OIV O Not Indeterminate

A:

Q: 2. Explain why f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths…

A: A number L is said to be the limit of a function f(x,y) as (x,y)→a,b , if for any real number ∈>0…

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: Evaluate the limit.

A: To find: limx→π6xsin3x

Q: Find the limits sin (Vr – 3) lim х — 9

A: Limit of a function is the value it tends to when the input value tends to some value. A limit is…

Q: Use continuity to evaluate the limit. 5 + Vx 28. lim sin(x + sin x) 5+x

A: To evaluate:   using continuity.

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

A:

Q: 4. Use the sandwich theorem to find the following limits: sin x (a) lim cos x (b) lim

A: a) -1≤sin x≤1⇒-1x≤sin xx≤1x⇒limx→∞-1x≤limx→∞sin xx≤limx→∞1x⇒0≤limx→∞sin xx≤0⇒limx→∞sin xx=0(using…

Q: 2 cos(4x) – 4x² – 2 lim *-о sin(2x) — х2 — 2х

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: 12, Show that the following limits do not exist. (а) lim 1 (x > 0), (b) lim (x > 0), x-0x2 x-0 Vx…

A: Given: d) limx→0sin1x2 to prove limit does not exist.

Q: Find the limits in Exercis

A: Given: L=limx→0x-xcosxsin23x

Q: 2. Use Squeeze Theorem to evaluate lim sin(sinh x) csch x 8118

A:

Q: Compute the following limits if they exist. sin x - (b) lim x→0 x tan x |

A:

Q: Find the limits in Exercis

A: To evaluate: limx→0sin5xsin4x Solution: Given,limx→0sin5xsin4x On simplifying further we get:…

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: Find the limits in Exercis

A: We can find the limit of an expression by applying the limit point to the variable in the expression…

Q: Find the limits in Exercise

A: Given, limθ→0cosπθsinθ we know expansion of sinx sinx=x-x33!+x55!-.... now put this expansion in…

Q: tan 11r a) limz 0 sin 3x

A: topic - limits

Q: Find the limits in Exercise

A: Given: limθ→π4tanθ-1θ-π4

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: Compute the following limits if they exist. sec x – 1 (a) lim x – sin x (b) lim x→0 x – tan x 2 - VI…

A:

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

A: Use L’Hôpital’s rule to find the limits limx→0+lnx2+2xlnx.

Q: Compute the following limits if they exist. tan x x - sin x (а) lim (b) lim (c) lim tan x sec x x3 |

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: Use l'Hôpital's Rule to find the following limit. 3 sin (x) – 3x lim 4x3 3 sin (x) – 3x lim (Type an…

A: I am going to solve the given problem by using some simple calculus to get the required result.

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

A:

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

A: We are allowed only 3 subparts of a question

Q: lim x→3 2+e* √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: Compute the following limits if they exist. sec x – 1 (а) lim x – sin x (b) lim I-0 x – tan r

A:

Q: evaluate using Theorem 2 as necessary.

A: We rewrite the given expression as:

Q: 2 cos(4x) – 4x² – 2 4. lim х-о sin(2x) —х2 — 2х

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: By using Sandwich Theorem, prove that lim sin r X-0 x

A:

Q: Use l'Hôpital's Rule to find the following limit. 3 sin (x) – 3x lim 3 5x 3 sin (x) - 3x lim ||(Type…

A: We have  to find the limit using l Hopital's

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

A:

Q: Evaluate using Theorem 2 as necessary.

A: Given: limx→0 x2sin2(x)

Q: lim x sin

A:

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.