What is the tangent of f(x)=cos(x),\at (0) ?

The tangent of f(x)=cos(x),\at (0) is y=-sin(a_{0})x+cos(a_{0})+a_{0}sin(a_{0})

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tangent of f(x)=cos(x),\at (0)

tangent of

f (x) = cos (x), at (0)

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, cos (a_{0}))

Find the slope of

f (x) = cos (x) : \frac{df ( x )}{d x} = - sin (x)

Compute the slope of

f (x) = cos (x)

x = a_{0} : m = - sin (a_{0})

Find the line with slope m=

- sin (a_{0})

and passing through

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

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

y = \frac{( 2 x + 1 ) ( x ^{3} + 3 )}{x}

4 x^{2} - 2 x + 3

\int_{0}^{π} sin (x) + cos (2 x) d x

y^{^{'}} + \frac{4}{5} y = 1 - \frac{1}{4} t, y (0) = 0

\int \frac{e ^{2 x}}{1 - e ^{x}} d x

What is the tangent of f(x)=cos(x),\at (0) ?
The tangent of f(x)=cos(x),\at (0) is y=-sin(a_{0})x+cos(a_{0})+a_{0}sin(a_{0})