(2{co(;)+ sin(;)})" Simpli fy, z = 1+v3i 0 22품 0 22플 O 42 O 24-

Q: sin (t) -dt 3 (4+ cos (t))?

A:

Q: 1. Find the derivative 4 ln 2) ³ 3x³ sin(2x) 5x2+3

A:

Q: S(csc x cot x + 9x°)dx Csc x + x° +c - sec x + x³ +c | CSc x + x9 - sin x + x³ +c sec x + r9 + c

A:

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: How would this parametric function of x=2cost +cos2t; y=2sint-sin2t be solved

A: In order to solve a parametric equation, firstly differentiate x and y with respect to t and then…

Q: Find the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: D cos( 5t D sinf see Dcost cast) 4

A: See the attachment

Q: Prove that sin(x + y) sin(x − y) = sin²x − sin²y. -

A: Formula's

Q: 2) Show that: cos (0) sin (0) (6) (5) - (² Xp = Yp sin cos (0) a))) ||rp|| cos (0 - a) -||rp|| sin…

A: This answer is given below.Explanation:

Q: Give an example of a value of z such that the equation sin(x ) = z is unsolvable.

A: We have to give an example of a value of z such that the equation sinx=z is unsolvable.

Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: (b) S tan3 x sec² x dx c) S sin³x cos5 x dx

A: The explanation of the solution is :

Q: 4 sec(8) = find cot(0) 2

A: Use trigonometric rations

Q: Let f(x)=sinx.When x=and dx=,then dy=? a) √2 b) cosxdx π+2 c) sin (+²) - sin() d) √2 √2 con()+sin()…

A:

Q: Sohe nin(x+y) + cos(x+y) Solve = sin

A:

Q: Consider a function f(x) where f" (x) = 5ª (ln 5)² + sin(- a) Find f"(x) dæ. b) Assume that f(0) = 9…

A: with the help of integration  properties we will evaluate the above function detailed solution is…

Q: -1 (3) cscx = sin X

A: We have to use proper substitutions and properties of analytic function.

Q: Find f), (b) f(r) tan(2r)

A: To find f’(x).

Q: 음 (sin-" (2))\_-+ = (교2)) | dx 2(:) A 1+ 2() B (C 2 (4) cos-1 (16) D -2 (금) cot () csc(6) CSC

A:

Q: 7) {(1- sin° 31)- cos3t dt 8) | t in’ (5x)· sec´ (5x) dx

A: 7) I=∫1-sin2 3t·cos 3t dt  ……1

Q: Q# (13 Rewrite: cos (x)sin(x)dx A) ſ u'du 1/2 B) Tu°du V312 C) [ -u°du 1 V3/2 D) [ u°du 1 V3/2 E)…

A:

Q: Evaluate D³(sinx - 4e²x) A -sin x-32e²x B -cos x-32e²x (C) с cos x-32e²x D sin x-32e²x

A:

Q: | sec(/I) tan(/) dr

A: We need to solve integral.

Q: 1 E valuate [ (x' + cos(3x)) dx sin (3x) a) b)

A:

Q: b) if J(zf64)} - 39ga) ) ce = Sin () %3D and S(3f (x)+9 6)) dx = tan () 2. 2. +596)) dx

A:

Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: Sx [x²cox dx U. V x² Sax - S(α (x²) [ cond) dx dx x² (sinx) - -S 2x Sinx dx U. V. x² sinx - [2x…

A:

Q: Solve the equation sin(x) - cos(x) =1. from[0,1].

A:

Q: Lim メートo Cos aX Cos bX

A:

Q: =4 and f = 12 and let g(x)=f(x)cosx. Find g 6.

A:

Q: Construct an equation such that y = = C1e3z cos x + C2e3ª sin x is its general solution.

A: To determine the differential equation from the solution  Check the number of constant in the…

Q: Solve y = x - 2ycot2x A B (C) D 2xsin 2x + (4y - 1) cos2x = C (4x - 1) sin2x + 2xcos2x = C (4x − 1)…

A:

Q: Cos (tan (-1)) nin (con (-4))

A:

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: -1

A: Given,

Q: 2) y = sin(3x²ex)

A: Find the derivative