Show that (x-2)2 -lnx = 0, [1,2] and [e,4] have at least one solution in the...

Show that (x-2)² -lnx = 0, [1,2] and [e,4] have at least one solution in the given intervals.

Expert Solution

Colby Messinger answered 2 years ago

For each of the following equations, find the general solution: (x^2)y′′+xy′+ 4y= sin(lnx) + sin(2 lnx)...

For each of the following equations, find the general solution: (x^2)y′′+xy′+ 4y= sin(lnx) + sin(2 lnx) y′′+y=tcost Thank you!

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0...

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0 3. Given that y1(x)=x is a solution of xy''-xy'+y=0 on (0, inifinity, solve the IVP: xy''-xy'+y=2 on(0,infinity), y(3)=2, y'(3)=1 14. solve the IVP: X'=( 1 2 3) X, X(0)=(0 ##################0 1 4####### -3/8 ##################0 0 1 ########1/4

L'Hospitals rule find the limits a) lim (tanx−secx) x→π/2- (b) lim (lnx-1) / (x-e) x→e...

L'Hospitals rule find the limits a) lim (tanx−secx) x→π/2- (b) lim (lnx-1) / (x-e) x→e (c) lim x^(1/lnx) x→0+

lim x approaches to 0 ( - cos (x^2) - 1) / e^x^4 - 1 Answer...

lim x approaches to 0 ( - cos (x^2) - 1) / e^x^4 - 1 Answer using l'hopital Please dont skip steps and be detailed with explanation

Show that the equation 4x3 + 2 = 5x2 + 2x has at least one solution...

Show that the equation 4x3 + 2 = 5x2 + 2x has at least one solution on the interval [0,1]. Then, show that the equation has at most one solution on the interval [0,1]. Lastly, show that the equation has at exactly one solution on the interval [0,1]. Thanks for the help in advance!

dervive the Frobenius solution to 4(x^2)*y"(x)+(3x+1)y(x)=0

4(a)Verify that the equation y=lnx-lny is an implicit solution of the IVP, ydx=x(y+1)dy &

4(a)Verify that the equation y=lnx-lny is an implicit solution of the IVP, ydx=x(y+1)dy y(e)=1 (b) Consider the IVP, test whether it is exact and solve it. x(x-y)dy=-(3xy-y^2)dx y(-1)=1 (c) Determine the degree of the following homogeneous function (i) f(x,y)=4x^2+2y^4 , (ii) f(x,y)=√5x^6-3y^6+4x^2y^4 ,

solve y' +(x+2/x)y =(e^x)/x^2 ; y(1)=0

1) Evaluate the integral from 0 to 1 (e^(2x) (x^2 + 4) dx) (a) What is...

1) Evaluate the integral from 0 to 1 (e^(2x) (x^2 + 4) dx) (a) What is the first step of your ‘new’ integral? (b) What is the final antiderivative step before evaluating? (c) What is the answer in simplified exact form? 2) indefinite integral (cos^2 2theta) / (cos^2 theta) dtheta (a) What is the first step of your ‘new’ integral? (b) What is the simplified integral before taking the antiderivative? (c) What is the answer in simplified form?

f(x,y)=30(1-y)^2xe^(-x/y). x>0. 0<y<1. a). show that f(y) the marginal density function of Y is a Beta...

f(x,y)=30(1-y)^2*x*e^(-x/y). x>0. 0<y<1. a). show that f(y) the marginal density function of Y is a Beta random variable with parameters alfa=3 and Beta=3. b). show that f(x|y) the conditional density function of X given Y=y is a Gamma random variable with parameters alfa=2 and beta=y. c). set up how would you find P(1<X<3|Y=.5). you do not have to do any calculations

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