thanks The following sets of functions are linearly dependent in F(R). Show this

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The following sets of functions are linearly dependent in F(R). Show this by expressing one of them as a linear combination of the others. (You may need to look up the definitions of the sin h and cos h functions as well as some trigonometric identities in a calculus book.) {3 sin2x, -5 COS2x, 119} {2ex, 3e-x, sin h x} {sin h x, cos h x, e-x} {cos(2x), sind2x, cos2x} {cos(2x), 1, cos2x} {sin x, sin(x + pi/4), cos(x+ pi/4)} {(x + 3)2, 1, x, x2} {x2 + 3x + 3, x + 1, 2x2} {In [(x2 + 1)3/(x4 + 7)], In , In(x4 + 7)}

Explanation / Answer

(a)119/3(3sin^2x)-119/5(-5cos^2x)-119=0

(b)0.25(2e^x)-1/6(3e^x)-sinhx = 0

(c) coshx-sinhx-e^(-x)=0

(d)cos^2x+sin^2x-cos^2x = 0

(e)cos2x-1+2cos^2x=0

(f)2^0.5sinx-sin(x+pi/4)+cos(x+pi/4)=0

(g)(x+3)^2 -9-6x-x^2 =0

(h)(x^2 +3x+3)-3(x+1)-0.5(2x^2)=0

(i)1/6(ln(x^2+1)^3/(x^4+7))-ln(x^2+1)^0.5 + ln(x^4 +7)=0

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