Question

Find an equation for the plane that is tangent to the surface z equals ln (x Superscript 4 Baseline plus y )at the point Upper P (0 comma 1 comma 0 ).

Answer 1

`z-y+1=0`

Explanation:

We are given that equation of surface

`z=ln(x^4+y)`

Point (0,1,0)

`z_x=(1)/(x^4+y)(4x^3)`

`z_x(0,1,0)=0`

`z_y=(1)/(x^4+y)(1)`

`z_y(0,1,0)=1`

Now, the equation of tangent plane to the given surface at point (0,1,0) is given by

`z-z_0=z_x(x-x_0)+z_y(y-y_0)`

Using the formula

`z-0=0+1(y-1)=y-1`

`z=y-1`

`z-y+1=0`