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Q: State and proof Rolle's theorem?

A: answer

Q: Quèstion 2 Find : 3 z z -z+2z if z=i -1 -5+3i 5+3i 5- 3i -5- 3i

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Q: The imaginary unit i is a number such that: Oit=1 Oi =V-1 %3D Oi² = - i %3D O²= - 1 %3D |

A: i=√(-1)

Q: cotA+tanA Prove that sec2A. cotA - tanA

A:

Q: O x = 8 tan(0)

A: Given that : The integral is ∫25x2 x2 + 64  dx .

Q: tane cote Prove =1 +tane +cote. 1-cote '1-tane

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

Q: UCLUI and BC. 21 The point (h, k) lies on the line y = x +1 and is 5 units from the point (0, 2).…

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

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: 1 Cos 2x =

A: Trigonometric equation

Q: integsate Sin ue go. 1og (Casu) where n-782

A:

Q: a) Prove Sin` 39 = 3 Sino 3 sine 4 Sin's %3D Hhence, find the valne 9 n the trianle? 30

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Q: yatant-t

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Q: a70 clam fB unif Cneiti mes on

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Q: Using Parseval's Identity, prove that: 1/(1^2)+1/(2^2)+1/(3^2)+1/(4^2)+......=(pi^2)/6

A: Parseval's identity is given as, 2|a|02+∑n=1∞an2+bn2=1π∫-ππfx2dx where   a0=∫-ππfxdx2π…

Q: Using Calculus, show thatsinn(x)dx Integrated from 0 to pi/2 is equal to ((n-1) / n) * sinn-2(x)dx…

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Q: 64. The complete cardioid r = 2 - 2 sin 0

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Q: tion to the differe where k is

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Q: sec* z tan' eda 3 Evaluate

A: Given integral, ∫sec5x tan3x dx

Q: a-X Tan" 1+ ax Differentiate

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Q: sin an n! n=1

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Q: 3. 2 csc 2x = sec x csc x

A:

Q: HoW/ Find all values (roats) of Thfollowing:. iz +1 = 2i e %3D %3D

A: Answer

Q: Using par seval identity show tha t Let fer)- e - Ests) Hiw P,リ+ %3D k/>

A:

Q: f(x) = tan x, x, = 0.04 %3D f(x,) f'(x,) f(x,) f'(x,) f(x,) f'(x,) 0.04 1. 2.

A: f(x)=tan(x) f'(x)=sec2(x)

Q: sen sen'x cos x de = sen'z (cos a dz) |sen'z d(senz) + C

A: To prove that: ∫sin2x cos x dx=sin3x3+C

Q: n+2 n+3 * ₁ (₁ - ¹) - ₂ (~ + ²) + + ₂ (²+ ³) + (n+¹) sin + sin sin n n lim n-x N + ... + sin (2) =…

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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: 9(cos x – 1) sin z cos a – sin a O 9 tan + 9 seca O 9 cotx + 9 csc x O 9 tan + 9 csc z O 9 sin x + 9…

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Q: Sin 26 de 9 sinte+4

A:

Q: Lim メートo Cos aX Cos bX

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Q: 元)27 sin= +icos- 9. 9 1+i 0+i 1-i 0-i II

A: We have to solve given problem:

Q: borun ind the integral 2. of 2.

A:

Q: jeta Prove that e-1 (1-e) ≤e- cos adx ≤ 1-el

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

Q: cot2 x- co

A:

Q: Sex)= é Sex) = e -sinx X、ニ-o.236 colculote X2=0,236 with solution ste Ps.

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Q: USing Inverse find Particular Solution of Differen tial ofera tor to 9 -48= Cosh (2X -1) + 3

A: We use following formula while calculating particular solution using inverse differential operator…

Q: 7 sin2 θ − 5 sin θ = 2

A:

Q: Green's theorem

A: Consider the given integral, According to the Green's Theorem, So the given expression can be…

Q: n[-5, 7), 1-cos x Find the absolute extremum point (s) of f(x) = e- if any.

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Q: sin 30 + sin³ 50 (7) Lim 1- cos y (8) Lim y→0 +sin? y² - y

A:

Q: Tan x = 2, x E [0,π\2]

A: we have to find value of x, in  tanx=2 where x∈0,π2

Q: cotx sinx + cotx= 0 O +n + 2nx O 0+n5, + 2n a O 0+2,- + 2n A 2 + 2n 7

A:

Q: +2+n-3 Simpli fy, O -1+ i" O -1+i O1+i O in+1

A:

Q: Scosx(bin x – sin’ x)&x. cos x(sin x – sin³x)dx. Evaluate

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Q: plicationS e Sum an s of th Verify that each eq Example XXI : 1. sec(T-) sec x 11

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: G(u, w) 3 sin (uи) at the point (7, +). Use symbolic notation and fractions where needed. Enter your…

A: We are asked to find the equation of tangent line in 3D.