Tangent Lines Find the equation of the tangent line of the curve tan(2x+5y) = x at (0,0).

Question: Calculus: Tangent Lines Find the equation of the tangent line of the curve tan(2x+5y) = x at (0,0). Pick ONE option

y = 5x

y=x

y = x/5

y=-x/5

Solution:

We have to find the equation of the tangent line of the curve

tan(2x+5y)=x

at the point (0,0).

Now, to find this, we have to find the value of

which is the slope of the tangent line, at a given point.

Here,

Differentiating both sides with respect to x, we get

Putting the value of x=0 and y=0, we can say that

So, the slope of the tangent will be -(1/5).

Now, at the point (0,0), the equation of the straight line is

So, the correct answer is option (D) .

Leave a Reply

Your email address will not be published. Required fields are marked *