**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) .**