() cos no = cos" 0 – cos"-2 0 sin? 0+ cos"-4 0 sin“ 0 () cos"-1 0 sin 0 cos"-3 0 sin 0 + 3. cos"-5 0 sin 0 – .. sin no
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- 1.An object whose temperature is 75^(@)C cools in an atmosphere of constant temperature 25^(@)C at the rate k theta where theta being the excess temperature of the body over the temperature.If after 10 minutes the temperature of the object falls to 65^(@)C find the temperature after 20 minutes.Find the time required to cool down to 55^(@)Cr Prove that (a) P_(n)(cos theta)=_(2)F_(1)(-n n+1;1;sin^(2)theta/2) (b) `P_(n)(cos theta)=(-1)_(2)^(n)F_(1)(n+1 -n;1;cos^(2)theta/2)a) solve over 0<x<360° for 4sin^2 x - 3sinx -1 = 0 cos x + sec x = 0 b) include restrictions for cos x + sec xintegral cos^7(4x)
- 1. Express as a sum or difference a.) sin 7t sin t b.) cos 6u cos (-4u) c.) cos 2t sin 6t d.) 2 sin 5θ cos 3θ e.) 2 sin 7θ sin 5θ f.) 3 cos x sin 2x g.) 5 cos 4u cos 5u(a) Find out the definite Integral, From 0.5 to 1.0 of Cos(x) dx. 1.0 ∫ Cos(x) dx 0.5 (b) Find out the definite Integral From 0 to 1 of Sin(x) dx. 1 ∫ Sin(x) dx 0Find all values of x in the interval [0, 2π] that satisfy(cos x)2 − 3 sin x − 3 = 0
- A s = e B s = cos(2) C s = e1/2 D s = e 2 E s = 1/e F s = sin(2) G s = π/4 H s = e−2 I s = ln( 2 ) A B C D E F G H I ∞∑n=0 1 -------- ( 2 )n n! A B C D E F G H I ∞∑n=0 (−1)n -------- n+1 A B C D E F G H I ∞∑n=0 (−1)n -------- 2n + 1 A B C D E F G H I ∞∑n=0 (−1)n ( 2 )2n+1 ---------------- (2n+1)! A B C D E F G H I ∞∑n=0 1 ------- n! A B C D E F G H I ∞∑n=0 ( 2 )n -------- n! A B C D E F G H I ∞∑n=0 (−1)n ( 2 )n ------------- n! A B C D E F G H I ∞∑n=0 (−1)n ( 2 )2n --------------- (2n)! A B C D E F G H I ∞∑n=0 ( −1 )n ------------ n!36 - With p0=0.5 and p1=pi/4 starting point f(x)=cosx-x, find its root when n=0 using Secant Method.A) 0.0483547563B) 0.967458574840C) 0.0909353635D) 0.30000000000E) 0.500000000cos^2ydx+(1+e^-x)sinydy=0
- 1. Given y = 4 cos(x) - x. Determine where the function is increasing in [-2, 7].Find all solutions to cos(7x)−cos(x)=sin(4x)cos(7x)-cos(x)=sin(4x) on 0≤x<2π30≤x<2π38.A spring–mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. If the system is driven by an external force of (3 cos(3t) − 2 sin(3t)) N, determine the steady-state response. Express your answer in the form R cos(ωt − δ).