b.T t sin t + 21

Q: n/2 csc t cot t dt

A: Given: Let I=∫π6π2csc t cot t dt To Find: To evaluate the given integration.

Q: Find r'(t). r(t) = 6 cos (t)i + 3 sin3(t)j + k r'(t) =

A: Let's find.

Q: Photo attached

A: Given:

Q: Find r'(t). r(t) = (tan (6t))i+t cos(t)j – Vik I| NOTE: Enter your answer in terms of i, j, and k.…

A:

Q: (b) у" — 2у + у 3 еt sin(z)

A:

Q: f (t) = 2e¬ + 4 sin t cos t %3D

A:

Q: Let r(t) = (sin t, 2 cos t), t = (a) Find r'(t). (b) Find T(t).

A:

Q: 8. t* – t² – t + sin v2t

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: "1 r(t) = ti + 1+ 12j + t²k 1+ t2 r(t) = cos? ti + sin? tj + tk %3D r(t) = cos ti + sin tj + cos 2tk

A: We can see that the graph is a closed one.

Q: Find r'(t). r(t) = (tan-(7t))i+t cos(t)j – Vēk

A:

Q: Find r'(t). r(t) = (tan-'(9t))i+t cos(t)j – Vēk NOTE: Enter your answer in terms of i, j, and k.…

A: We can solve this as follows:

Q: 1) sin C

A:

Q: calculate r'(t) and T(t), and evaluate T(1). r(t) =〈cos πt,sin πt,t〉

A: Given :                   r(t) = cos πt , sin πt , tDifferentiating with respect to t, we get…

Q: N(t) at the given point. cos(t)i+ 6 sin(t)j+ tk; t = 2

A:

Q: ∫ t2 sin(t) dt

A: Explained below...

Q: b. " +r = 2 cos t

A:

Q: 9) f(t)=tu,(1) 10) f(t)=u,(1)sin(t)

A:

Q: 1 g(t) = –4 sin t – 4sec²t – 5 csct cot t + 5et + - - - V1-t2

A: We know that the indefinite integral of the sum of functions is equal to the sum of the indefinite…

Q: Find r'(t). 13 r(t) = 3 cos (t)i + 5 sin (t)j + k %3D r'(t) %3D

A: Given:

Q: a) L{t.sin(t– 7)U(t-)} = ? 2 L{[(t-u) e* du} =? b)

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: a:1 c R E4 t a(t) = (cos (), sin (), 2, at) %3D ↑

A: Given the curve  α:I⊂ℝ→ℝ4 given by t→αt=cost2, sint2, 2, αt

Q: Find r'(t). cos 4 cos³(t)i + 2 sin³ (t)j + k r(t) = 4

A:

Q: f(t) = sin(37t), -1<t<1 %3D

A: Given function is: ft=sin3πt  ,   -1≤t≤1

Q: Cos t sin t Set A and x = [a b]T. Demontrate that ||Ax||2 = a² + b². %3D

A:

Q: 12. r(t) = (cos t +t sin t)i + (sin t – t cos t)j, T/2 <ts TT %3D

A: To find the arc length parameter for the given parametric curve in the given interval

Q: g(t) = t sin t

A:

Q: 10. r (t) = (2 cos t, 3t, 2 sin t)

A: Solve the following

Q: Find r'(t), r"(t), and r'(t) • r"(t). r(t) = 7 cos(t)i + 9 sin(t)j

A:

Q: Find r'(t). r(t) = (tan-'(5t))i+t cos(t)j – Vik NOTE: Enter your answer in terms of i, j, and k.

A: r(t)=tan-1(5t) i+t cost j -t kddt tan-1(5t)= 11+(5t)2 ddt(5t)ddt tan-1(5t)= 51+25t2 ddtt cost=cost-t…

Q: ind r. f'(t) = sec(t)(sec(t) + tan(t)), = -3 f(t) Need Heln? Read It Watch It

A:

Q: 21. dridt + r tan t = cos? t, r(T/3) = 1 Answer: r= cos t( sin t+ 2 - V3/2)

A:

Q: ha)= Jo So Sin't dt

A: We have to find the given integral .

Q: M{sin x; p}

A: We have to evaluate M{sin x ; p} and M{cos x;p} We know that, Me-ax;p = Γ(p)ap De Movire's Theorem:…

Q: F(t) = 3 cos(t)ỉ + 3 sin(t)j + 2tk

A:

Q: au, a'u +: Q3) A: Find u = In(x + y) + tan () where

A:

Q: 3T <B<T 2으 Sin a= - 29+2 2-a<27itan B=

A: Given,          sinα=-2029 , 3π2&lt;α&lt;2π          tanβ=-34 , π2&lt;β&lt;π

Q: 7) f(t)=e"(Acos(ßt)+B sin(ßt)) -at

A:

Q: Find r'(t). r(t) = 3 cos (t)i + 4 sin°(t)j + k r'(t)

A: Given, r(t)= 3cos³(t)i + 4sin³(t)j +k

Q: F k d

A: Use conic section we can prove it.

Q: cos t dt 1 + sin t 37.

A: The given integral,37. ∫cos t1+sin tdt

Q: f sin(t) 3 and t 8. %3D

A: in 2nd quadrant sin is positive and cos is negative.

Q: c(t) = (sin 2t, sin t), 0<t < n.

A: Solution Given c(t)=(sin2t,sint),0&lt;t&lt;πUsing Green's Theorem , calculate the area of the region…

Q: s(1) =sin(r' – 1)

A:

Q: Find r'(t). r(t) = (tan-(4t))i+t cos(t)j – Vik NOTE: Enter your answer in terms of i, j, and k.…

A:

Q: Find r'(t). r(t) = (tan(6t))i+t cos(t)j – VEk NOTE: Enter your answer in terms of i, j, and k. r'(t)

A:

Q: V2 sin(t)=2cos(t) sin(r)

A: Given query is to solve the trigonometric expression.

Q: 4- f(t) = St sin(t) e-5tdt

A:

Q: Find r′(t). r(t) = ⟨t sin t, t cos t, t⟩

A: (uv)'=u'v+uv'ddxsin x=cos xddxcos x=-sin x

Q: b) f(x) = sin(T

A: Trigonometric Fourier series of (b)

Q: Let 7(t) = (t2, sin t – tcos t, cost +t sin t). Find T and K 4 12. В 4

A: Given : r(t) = ⟨t², Sint - t cos t, cos t + t sin t ⟩