90) |(tan 2z)? sec 2r dz 21) / dr

Q: Show the only soution to ax = 1, a + 0, is x = a^-1|

A:

Q: If y=tanx, Prove that Y™ 2 (Y²+1)(3+1)

A: We will find the required.

Q: In [tan (5 + )| +o sec x dx 4 2

A:

Q: 3. Suppose csc(A) 2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII 4

A: The relation between the sides and angle of right angle triangle are expressed in the ratio called…

Q: 11. Use the substitution u = x/3 to prove dx tan 9+x2

A: Consider the integral

Q: tan u du = In | sec u| + C

A:

Q: =-i In (izt Ji-z2?) Sin 군 tan 군 = 늑In

A:

Q: Prove thiat dx Ś (areten()) ) = し 4+X

A:

Q: Evaluate the integrals

A: Consider the integrals 31)    ∫0π/27costsintdt32)    ∫0π/413tantsec2tdt

Q: 7) In AXYZ, mLY 80, XY = 14, and XZ 17. To the nearest tenth, what is mLZ? %3D

A:

Q: 17. [sec u] = (sec u tan u)u' dx

A:

Q: Jósec? 30/3+2 tan 30d0 8.

A:

Q: Suppose that x = 2 tan 8. What is sec e equal to in terms of x? √4+x² 2 √4+x² X Option 1 Option 2…

A:

Q: Show that cosh iθ = cos θ,

A: We know that  coshx=ex+e-x2 and by Euler's theorem, eix=cosx+isinxe-ix=cos-x+isin-x=cosx-isinx We…

Q: Find the areg between Ye CosX an d y--SinX trom o tr .

A:

Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

A:

Q: Q. Use first principle rule and proue that secn tene if y = secx %3D

A: Note  your Question is wrong because right Question is  y=sec(x) then y' = sec(x)tan(x)

Q: Prove by mathematical induetion. Ine I+2 +2+2 +2° = 2.

A:

Q: 2) Eliminate the arbitrary enstant, 4 y= x*+ Cix + Cz e-X

A: Given problem:- Eliminate the arbitrary constants. of y= x² + C₁x + C₂ e-x

Q: 3. Prove that: tan-1z +z %3D

A:

Q: what is Selution of DE (D-20)Y=ê Sinx When Sotved using the meth ed of undetermind

A:

Q: o what does it con s conditionally conv 1. onvergence for at is the radius of approximation of e √2,

A:

Q: If tan-0 = 1- a Prove that sec® + tam Ocosece = (2- a) 3. %3D %3D

A:

Q: ove that 1 cosh(tanh) = -1 -1 < r < 1. V1- 2

A:

Q: et A be 4X4r nas non-brivial . -son-

A:

Q: What is tanh (Ei) O V3 V3i O 13

A:

Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: Inand consicr HeLines (tn) venfy Al-5,-6) isapoint of (d) 2) prme Hat (4,)-b de] 3) Cans tract (d1)…

A: Since your question contains multipart, we solve only 1,2,3. If you need any particular question…

Q: Prove (05t - sin 4t tos?t

A:

Q: (x) = 3x +12x+2, %3D ues of a, b and c such that

A:

Q: 7 cos(z) Driented ris countercleckwise ortented rectangle with -2-i , 2-i, 2té, -2ti

A: Contour integration

Q: See attached image. Please provide a solution with a detailed explanation of steps.

A:

Q: Prove that osIl" + sini = tan s 56° cas 11-sinll %3D

A: -To show:cos11o+sin11ocos11o-sin11o=tan56oBasic formula needed:-tan(A+B)=tanA+tanB1-tanA.tanB…

Q: 1 .Prove that : sec q + tan q = 2x or, 4x If sec q = x+ 2x

A:

Q: secx + 1 51. secx - 1 (cscx + cotx)? %3D 52 56 verify that the equat

A:

Q: Suppose you Know that tand 3/12. Vsing this infe, de tevmine cuhot quadiantdis in dnd Caliulate…

A:

Q: 7) [[3embch5y] dvl [jel*5) dy] „In[sec h 5y]

A: Using rule of logarithm &amp; integration formula of sech(x)

Q: Let fla)= é cosx, s** %3D Express your answers in exact form.

A:

Q: - [Mesin(2x) dx = esin(2x) + C_then the Mis equal to +C,t

A:

Q: 11T |13T V2 - V6, determine the value of sec 60. Given that sec 12 %3D 12

A:

Q: pes of animals are treated by at least on r. Scott, and Dr. Baker)?

A:

Q: If [ In(ax)dx = 3, then a %3D 1

A:

Q: (6) Given that In= tan" x dx, show that, for n 2 2. %3D In- In-2 = %3D n- 1

A: I think given question is slightly wrong. According to me the required proof should be…

Q: vsin ax (02+4)4= sin x is the fun ction with y %3D

A:

Q: 5) why is x3- 3x +I X +2 Conti nuous (0,00) on where is it discontinuous?

A:

Q: S- cos ve ve sin? ve de =

A: We will evaluate the given integral.

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.