Determine : L[te t sin 10 t]. 20s 20(s +9) (s² +100)? [(s +9)? +100]? A.) B.) 20s 20(s +9) (s+9)(s² +100)² (s+9) +100

Q: T/4 ttant dt 2+ cos t -7/4

A:

Q: 2cos'z = COS T Select all correct solutions.

A: Follow the procedure given below.

Q: Q3:- If x= sec 0- cose and y = sec" 8- cos" 0 Prove or disprove that (x2 + 4) ) = n2G2+ 4) %3D

A:

Q: Find 7'(t), given ř(t) = ( – 4cos( – 5t), 3 sin( – 5t), e*). - - F (t) =

A: Solve the following

Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: sin, ifx T 2л

A:

Q: 29 - For what values of a and b is | S x+3a-b axt 26 3x-5 Continuows at every X?

A: g(x)=ax+2bx≤0x2+3a-b0<x≤23x-5x>2

Q: Show that g(t) = t² tan t takes on the value for some t in [0, 4J.

A: Given Data The equation is g(t)=t² tan t. The interval is [0, π/4].   Put the value for t=0 in…

Q: Which of the following equations is FALSE? * O tan t = tan (t + 2m) where t n/2 + kTI O tan 2t = tan…

A: tant+2π=tant+tan2π1-tant·tan2π    ∵tanx+y=tanx+tany1-tanx tany=tant+01-tant·0=tant Therefore…

Q: Solve the diferential egyatien dy - by Melne's méthool with h-o-1 e Cosx dx

A: GIVEN: y'=e-xcosx-y   The formula is: yn+1,p=yn-3+4h32yn-2'-yn-1'+2yn'    ............(1) Put n=3,…

Q: Transform F(s) (giving you cos 5t + t³

A:

Q: use (10.10.1) to determine L[f]. Q.f(t)=sin2 at, where a is a positive constant.

A: Given data:     The given expression for the Laplace is: . The given function is: f(t)=sin2at.…

Q: f (t) = 4 cos(4t) – 9 sin(4t) + 2 cos(10t) (As* + Bs3 + Cs² + Ds + E) Fs) Fs4 + Gs3 + Hs² + Is + J

A:

Q: (a) Find out solution of the following 3rd order ODE: y" – 4y' – 4t + sint – tet = 0 - -

A:

Q: -3t 10. s = cj e" + c2 e" cos 51 + cz e" sin 51 + 123 O Sm + 5 Su + 17 s - 123 s = 100 O Sm + 17 Su…

A:

Q: = cos(x + y), when x = 0, y = " %3D

A:

Q: Solve 2 cos (t) - con(t) – 3 = 0 for all solutions. where ke Z

A: solution of the eqauation

Q: 8- Evaluate a) Sz? + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) S 3x. csc² dx x3-9x2+8

A:

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

A:

Q: 2.xy x² – y? Show that - = 0 if z= Tan

A:

Q: Provide an appropriate response. Find f(n) if f(t) dt x sin 8x.

A:

Q: Evaluate: S2-* tanh21- dx 4. A. –In2 In | cos h21- |+C C. In | sec h21-x | +C In 2 B. -4ln | sech?…

A: We are authorised to solve only one question, please repost remaining questions. Indefinite…

Q: 6- What is the arclength of the function y = 7x + 2 on the interval [2,6]? a) O /2 90406 b) O 20 c)…

A:

Q: az a2z az a2z at ax2 23. If z = sim(x+ sint), show that дх дх дt

A: Given,Z=Sinx+sintto prove∂z∂x·∂2z∂x∂t=∂z∂t·∂2z∂x2

Q: By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

A:

Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

A:

Q: Solve 3 tan(z) = V3 over the interval [0, 27)

A:

Q: Te 2=tnx then prove thot dx 28 Snメー tty? 1+xて

A: We have to use proper calculus applications.

Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

A:

Q: 5(t - )cos3t) 3 252 + 18

A:

Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

A:

Q: Q2// Given that oc= = sec-(-V13/2), find sin x, cos x, tan ox, csc o and cot x.

A: Given: write as Formula used

Q: 2 f(t) = ( tv4t2 + 1, sin(t) cos² (t), t2 + 1

A: As you ask parts b and c. in part b we need to find the equation of the tangent line to the curve at…

Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

Q: Evaluate 7(t) dt: 4 4t -k; a = 0 and b = 4 t2 +1 †(t) -î + 2e4t cos t ĵ- t2 + 5t +6

A:

Q: d 1 - (sec-!r) = dx Prove that xVx - 1

A: Let y=sec-1xsec y =xcos y =1x.....1 Thus sin y=1-cos2y=1-1x2=x2-1x2=x2-1x .......2

Q: f (t) = 4 cos(4t) – 9 sin(4t) +2 cos(10t) (As* + Bs3 + Cs² + Ds + E) Fs) Fs4 + Gs3 + Hs² + Is + J

A:

Q: show that1) d/dz [cosz] = -sin z

A:

Q: Find L {(2 – t) (5 cos 3t – 1)}. 1 g3 10 + s2 +9 - - s2 s(s²+9) O 1 s3 10 + s2 -9 2 - - 8(s2 –9)…

A:

Q: 2- FIND f (t) or fis) AS APPRO PRIATE A) L}Je costdt COS ) y+2メ=8(t-)0)00)=イ

A: Here we use basic definition of Laplace transform

Q: Use the Intermediate Value Theorem to show that the equation  t^2 - cos(t) = 0  has at least one…

A:

Q: Solve the eaation on the interval. 2sin Đ =3(cos o t D

A:

Q: use (10.10.1) to determine L[f]. Q. f(t)=sin2t

A: Known facts: ∫eatsinbt dt=eata2+b2asinbt-bcosbt+C   Substitute ft=sin2t in Fs=∫0∞e-stftdt and…

Q: Prb $2 x sinx dx メt)

A: We have to Solve given Improper Integral using Residue Theorem as Follows :

Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

A:

Q: 211 If f(x) = sinh(- In c) then f'(r) 27

A: Given,        fx=sinh-lnx

Q: Q1/ Sketch x1[n] , x2[n] , x3[n] where : x1[n] =Sin(rtn) , x2[n]= e^( n), x3[n]=x1[n] - x2[n]

A: Graph of sin(πn)

Q: H.co/ prove That;. dz 1-2 Cosh2=

A:

Q: Is this correct?

A: