What is the tangent of f(x)=3sin(x-2) ?

The tangent of f(x)=3sin(x-2) is y=3cos(a_{0}-2)x+3sin(a_{0}-2)-3cos(a_{0}-2)a_{0}

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tangent of f(x)=3sin(x-2)

tangent of

f (x) = 3 sin (x - 2)

y = 3 cos (a_{0} - 2) x + 3 sin (a_{0} - 2) - 3 cos (a_{0} - 2) a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 sin (a_{0} - 2))

Find the slope of

f (x) = 3 sin (x - 2) : \frac{df ( x )}{d x} = 3 cos (x - 2)

Compute the slope of

f (x) = 3 sin (x - 2)

x = a_{0} : m = 3 cos (a_{0} - 2)

Find the line with slope m=

3 cos (a_{0} - 2)

and passing through

(a_{0}, 3 sin (a_{0} - 2)) : y = 3 cos (a_{0} - 2) x + 3 sin (a_{0} - 2) - 3 cos (a_{0} - 2) a_{0}

y = 3 cos (a_{0} - 2) x + 3 sin (a_{0} - 2) - 3 cos (a_{0} - 2) a_{0}

\int \frac{9}{4 - x ^{2}} d x

x \to 0 lim (2 - x)

x^{\frac{4}{3}}

f (x) = x^{- \frac{2}{3}}

\frac{d y}{d x} = \frac{y}{2 x}, y (4) = 1

What is the tangent of f(x)=3sin(x-2) ?
The tangent of f(x)=3sin(x-2) is y=3cos(a_{0}-2)x+3sin(a_{0}-2)-3cos(a_{0}-2)a_{0}