Question

An equation for a tangent to the graph of y = arcsin x/2

A) y = -2x
B) y = -x
C) y = 2x
D) y = x

Answer 1

The equation for a tangent to the graph of y = arcsin(x/2) can be found using the derivative of the function. The equation of the tangent line at a point (a,b) on the graph is given by y - b = (1/sqrt(4-a^2))(x - a).

Step-by-step explanation:

The equation for a tangent to the graph of y = arcsin(x/2) can be found using the derivative of the function. The derivative of arcsin(x/2) with respect to x is 1/sqrt(4-x^2). So, the equation of the tangent line at a point (a,b) on the graph is given by y - b = (1/sqrt(4-a^2))(x - a). Simplifying this equation gives us y = (1/sqrt(4-a^2))(x - a) + b.