sin²k Σ 2* k = 1

Q: IRI- 2. <| sinz|< -e 2

A:

Q: sin² 2 (KTT) сс 2 Σ (***)_ ~*(+)) k4 k=1 8k

A: We have to solve the series.

Q: Find the limit.

A:

Q: 2 sin²(x) – 3sin (x) + 1 = 0

A:

Q: 1-sin t lim 1+cos 2t t- 2

A:

Q: (1+sin2x)/(sin2x)=1+(1/2)(sec x)(csc x) prove identity

A: Left hand side:1+sin(2x)sin(2x)=1sin(2x)+sin(2x)sin(2x)=1sin(2x)+1=12sin(x)cos(x)+1  [using double…

Q: sin (20) 2 J 1+ sin² (0)

A:

Q: d Proof Prove that [cos x] dx - sin x. -

A: To prove ddxcos x=-sin x. In order to prove the given derivative, use the definition of derivative…

Q: いpO O siniz iff Z-kTi,K-o,っ3リーー Sin iz ニ

A: we have to prove that siniz=siniz¯ if and only if z=kπi, k∈ℤ.

Q: tan 0 (2) Lim = 1 %3D

A: We first expand the series of tan x and then proceed as explained below:

Q: Sin 0/1 + co² B) 2.

A: sinθ1+cot2θ                             =sinθ1+cos2θsin2θ…

Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

A:

Q: sin x(cos x-1) 8. Prove sin(n -x) – tan(t + x) | COSX

A:

Q: () 1 (k) I-3 (1) sin(@)- sec2(0)

A:

Q: sin(x) 4. lim x→0 1 – cos(2x)

A: The solution of the problem is given in the next step.

Q: sine 2. Co s+1 J9-x2 5. 5 + x² Q4 メP 2.

A: Please refer the attached image for complete solution. Given: four integralsTo calculate:…

Q: sin 1(e") 2. lim (- V1-e2

A:

Q: tion to the differe where k is

A:

Q: n Σ 6. lim sin -JT - - n→∞ n n i=1

A: 6. Given question is , limn→∞∑i=1nsinπin-ππn The given sum is written in form of ,…

Q: DIFFERENTIATION: MPLE If 3 find つく- 31 Sinx= es expansion for cos3x

A:

Q: sin ( 27 +1)x Prove that dx =7 for all ne N. Sin x

A:

Q: calcu late an approscimation of with an Sin a ervar of less than 10 イイ

A:

Q: sin²(x ) jai' (x ) X 3 1

A: The objective is to find the integral, ∫1∞sin2(x)x3dx

Q: lim »0 sin(2t) tan(7t) is t2

A: Here we find the value limt→0sin(2t) tan(7t)t2

Q: sin6x 3 - lim 0 sin2x O 1/3 O 1/2

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

Q: sin 3n 3"

A:

Q: 6. f(1) =-e" sin (21 + 7 ) 3t -2t

A:

Q: lim-o t- sin 3t² 1-cos 2t

A:

Q: A 70 (x) -(5n4x) 140° (sin

A: The given data is: [12x-18sin4x]40∘70∘  To find the value of the given data.

Q: tan x 4. a) Evaluate dx. In (cos x) b) Evaluatef e4*x3 dx.

A:

Q: 4 sin² x - 1 2 sin x + 1 2 sin x - 1

A:

Q: Cosh A In(x

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

Q: 2. 2) tan- 1 4) sin- 6) tan-1 V3 -1 01_ V3 10) sin -1 2. 12) tan-! 3.

A:

Q: Find the limit

A:

Q: sin 2x J-1 x* +x* – x² +2

A: Here we have to find the integration: ∫−11sin2xx8+x4−x2+2dx

Q: sin(4z) 7. lim I-0

A:

Q: sin 4x2 lim 1 cos 6x

A:

Q: tan-1 z = 1 – j2

A:

Q: sin-1(e* 2 lim V1 - e2x x→0-

A:

Q: a) = Cos(x + a); prov

A: we have ,  sin(x-α)=cos(x+α)we have to prove that, tanx=1

Q: (sin(x), x 4 x, k(x) = f(x) = -x2 + 4x – 2, х — 6,

A: Consider the given function as fx=sinx     x&lt;0x         0&lt;x&lt;2-x2+4x-2…

Q: -1 -sec"(x) =: dx -csc"(x)= Explain why the modulus x Given that and dx is needed here.

A: Definition used -                                        ddxsecx =secxtanx…

Q: lim t→0 of tan4t/sin2t

A:

Q: separable 9-X(2lnX+1) Sin y+ ycosy

A:

Q: 4. lim sin2ß B-0 sin3ß

A:

Q: Sin 3x = 3sinx - 4sin'x

A:

Q: sin 20 7. lim n sin 0 tan 0 6.

A: We can solve it using the properties of limit as below

Q: 13). lim n Sin (号)

A: We find limit of given sequence