Question

Show that there is a solution to the equation e^x=3-2x in the interval(0,1)

Answer #1

for the equation f(x) = e^x - cos(x) + 2x - 3
Use Intermediate Value Theorem to show there is at least one
solution.
Then use Mean Value Theorem to show there is at MOST one
solution

Show that the equation f(x) = sin(x) - 2x = 0 has exactly one
solution on the interval [-2,2]

Find the average value of the function on the given
interval/
f(x) = 2x^2 . e^(2x) , [0,1]
the average value is ………… ( round to 3 d.p)

Use intermediate theorem to show that theer is a root of
f(x)=-e^x+3-2x in the interval (0, 1)

a)
Let y be the solution of the equation y ″ − y = 3 e^(2x)
satisfying the conditions y ( 0 ) = 2 and y ′ ( 0 ) = 3.
Find the value of the function f ( x ) = ln ( y ( x ) − e^x )
at x = 3.
b)
Let y be the solution of the equation y ″ − 2 y ′ + y = x −
2
satisfying the...

Find the differential Equation of
xy'-2y+(2x^3)e^-x=0

differential equation one solution is given,
xy''-(2x+1)y'+(x+1)y=x^2; y_1=e^x

Show that f(x) = C1e4x +
C2e-2x is a solution to the differential
equation: y’’ – 2y’ – 8y = 0, for all constants C1 and
C2. Then find values for C1 and C2
such that y(0) = 1 and y’(0) = 0.

show 1/(x^1/2) is not uniformly continuous on the interval
(0,1).

find the upper bound of the LTE (euler)
2x'+2/3 x = 4x^2
and the interval for t is [0,1].

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