r(t) = 4 cos(t)i+4sin(t)j; t = 3 /3 1 2/2' 2/2 -V3 2/2' 2/2 1

Q: 1. [(5x --3 )dr

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

Q: Find the following for the given equation. r(t) = 5 cos(t)i + 5 sin(t)j (a) r'(t) = (b) r"(t) =

A:

Q: (c). f(z) = (x + 5 sin z) (1 - 7 cos z)

A:

Q: L x? 8(x – a)dx L7t? cos t 8(t)dt 7t² cos(t- 2) 8(t – 2)dt

A: Given that Dirac delta function problem . We know that Dirac delta function property and use…

Q: EVALUATE 3 x2 +1 cos dx -1 dx x2 +1 А. cos В. О C. 2/ cos 3 dæ x2 +1 D. 1

A:

Q: dy ? dx If sin(x + y) = xy, what is the expression for cos(x + y) – y x – cos(x + y) (A) cos(r + y)…

A:

Q: Find T(t) and N(t) at the given point. r(t) = 7 cos(t)i +7 sin(t)j; t = 3 T(-) .3 .3. ||

A:

Q: i. L x² 8(x – a)dx ii. L,7t? cos t 8(t)dt L,7t? cos(t – 2) 8(t – 2)dt iii. -

A:

Q: Find z(t) for X(s) = 8-2 %3D $(s+ 1)(+9) Select one: O a.z(t)3D-86(0) + 금etu(e)-뷰.e 2.cos3t. u(t) +…

A:

Q: Let r(t) = cos(t) i + 4 ln(t² + t)j + 5 tan¯¹(t) k. Find 7' (t).

A:

Q: COS πx dx S1n, πx

A:

Q: Find r(t) and v(t) if a(t) = 8 cos(t)k, v(0) = 4i + 6j, and r(0) = 7i. v(t) r(t) %3D

A: We have given: at=8cost kv0=4i+6jr0=7i We know that at=dvtdt So, we can write this as: dvt=at…

Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to…

A:

Q: 3. Express the following function in terms of 'Sine & Cosine'; y (t) = 4 sin 2nt + 15 cos 2nt [

A: please see the next step for solution

Q: dy If y = sin(6x – 4), then dx O a. 4 cos(6x – 4) O b. -4 cos(6x – 4) 6 cos(6x – 4) O d. -6сos(6x -…

A: y= sin(6x-4)

Q: S sin(x - 1) cos(x² 2 + 7Jdx

A:

Q: 1. / 3 cos³ x sin? x dx

A: NOTE : As per our guidelines we are supposed to answer only one question . Kindly repost other…

Q: T/2 T (² cos 2y + 3y° sin z) dz dy . Evaluate -1/2 Jo

A:

Q: [a csc ()- y] do + ædy = 0 CSC O y= x cos(In z) + C O y=D cos (In a + C) O In + cos(E)= C O Ino COS

A:

Q: Evaluate 4x³ sin² (x¹) dx + C

A:

Q: Q.21 find the order and degree for the following ODE's: 1) xy =sinx O5 - y(x) =cos(3x) dx 2)

A:

Q: Find f. f(t) = 5e¹ - 6 sin(t) — 5 f"(t) = 5et + 6 sin t, f(0) = 0, f(π) = X 0

A:

Q: 2 S² T ㅠ 1-cos x dx 2

A:

Q: Simplify your expressions for xM(t) = 0.5 cos + 9cos ( & ym(t) = 0.5 sin + 9sin xM(t) = B cos(kt +…

A: xM(t) = 0.5 cosπt3 +9cos πt6yM(t) = 0.5 sin πt3 + 9 sin πt6 XM(t) = B cos(kt + β)YM(t) = C sin(kt +…

Q: 7T, 0 cos( {*) cos(2y)dx 2gin( gx) sin (2) dy 77

A:

Q: Solve the problem. For what values of t is r(t) = cos t i + sin t j + sqrt( 9- t2) k continuous?

A: A vector-valued function r(t) is continuous at t=a if and only if: 1. r(a) is defined. 2. limt→ar(a)…

Q: Evaluate x/12 0 14√/1- cos 12x dx.

A: Given, ∫0π4141-cos12xdx

Q: r(t) = (5 cos (t), 5 sin(t), 3 sin²(t)) at t ¹ (7) = ㅠ 4

A: