What is the tangent of x+2sin(x) ?

The tangent of x+2sin(x) is y=(1+2cos(a_{0}))x-2a_{0}cos(a_{0})+2sin(a_{0})

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tangent of x+2sin(x)

tangent of

x + 2 sin (x)

y = (1 + 2 cos (a_{0})) x - 2 a_{0} cos (a_{0}) + 2 sin (a_{0})

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} + 2 sin (a_{0}))

Find the slope of

y = x + 2 sin (x) : \frac{d y}{d x} = 1 + 2 cos (x)

Compute the slope of

y = x + 2 sin (x)

x = a_{0} : m = 1 + 2 cos (a_{0})

Find the line with slope m=

1 + 2 cos (a_{0})

and passing through

(a_{0}, a_{0} + 2 sin (a_{0})) : y = (1 + 2 cos (a_{0})) x - 2 a_{0} cos (a_{0}) + 2 sin (a_{0})

y = (1 + 2 cos (a_{0})) x - 2 a_{0} cos (a_{0}) + 2 sin (a_{0})

f (x) = \frac{x}{x ^{2} + 9}

\int_{0}^{π} e^{x} cos (x) d x

n = 0 \sum \infty \frac{5}{3 ^{n - 1}}

x^{\frac{1}{5}}, x^{\frac{1}{2}}

x^{^{'}} + x = 0, x (0) = 1

What is the tangent of x+2sin(x) ?
The tangent of x+2sin(x) is y=(1+2cos(a_{0}))x-2a_{0}cos(a_{0})+2sin(a_{0})