(a) | Show that tan- z = in() = n 1, і —z i + z -In i - z -In z +i %3D | - (b) values of tan-(2 + i). ] Use part (a) to find all the

Q: The set of functions {sin nx}, n = 1, 2, 3, ... , is %3D orthogonal on the interval [ -n, n]. Show…

A: Given- The set of functions sin nx, n = 1, 2, 3, ⋯, is orthogonal on the interval -π, π To Show-…

Q: Q: Prove the following identitie: (1+tan A tan B) +(tan A - tan B)* = sec' A sec' B.

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Q: +siny+x

A: Side View

Q: -1 a) y = x tan 2x 4 4x +. b) In(x+y)=Dtan (xy) c) y=e* cos x d) x +xtany = e e) y = Vz sin (z)

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Q: Evaluate the integral 1/3 El+ secx tan x dx

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Q: x-1 c) Let f (x) = x+ 0. Find by using numerical calculations in a tabular x2 - 1 which x approached…

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Q: f(seca tan a – 8a")da tan a + a° + c sec a +a8 +e - sec * – a8 +c sec a – a° +e sec a +8

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Q: 2/ A) Prove the identity Sin (A + B) + Sin (A - B) = 2SinA cosB B) Find real numbers x, y, z for the…

A: The trigonometric functions can be proven by using trigonometric identities. The trigonometric…

Q: 3. ſsec? x(1+ tan x)/tan x – 1 dx ans : 3 (tan x – 1)' + ¿(tan x – 1) +c 4. S'cos x(2+ sin x)/2 +…

A: 3. Given integral is ∫sec2x(1+tanx)tanx-13dx Substitute tanx-1=z⇒tanx=z+1sec2xdx=dz Therefore, the…

Q: 1 /₁+422da dx 1+ 4x2 15. Evaluate (a) tan-¹(x) + C (d) tan-¹(2x) + C -1 (g) tan-¹(x) + C (j) None of…

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Q: Algebraically prove these formulas are true  r^2=x^2 + y^2 tan theta = y/x

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Q: n lim >(sin (2mx;))Ax over [0,1] i=1

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Q: what is the domain and range of f(x, y, z) = x + ln y + cos z (please explain)

A: The given function is:f(x, y, z) = x +lny +cos z x is defined for all real numbers. So The domain of…

Q: x² + 9 dx J x2 – 1)(x² + 4) | In \x + 1| + In |x – 1| +; tan-1 (-) + c -In |x + 1| - In |x – 1| -;…

A: Topic:- application of integration

Q: Given that z = 1- iv3, express z in the form r(cos 0 +i sin 0). Hence write down z' in the form…

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Q: w wor

A: Here we have to evaluate I=∫ln(sin(x))cos2(x)dx ...................(1)

Q: Prove sin (x + y) tan x + tan y sec x sec y

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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.