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

Answer:

$z-y+1=0$

Step-by-step explanation:

We are given that  equation of surface

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

Point (0,1,0)

$z_x=\frac{1}{x^4+y}(4x^3)$

$z_x(0,1,0)=0$

$z_y=\frac{1}{x^4+y}(1)$

$z_y(0,1,0)=1$

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

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

$z=y-1$

$z-y+1=0$