Question

hey can someone help me with these i need help


Consider the curve given by x2 + sin(xy) + 3y2 = C, where C is a constant. The point (1, 1) lies on this curve. Use the tangent line approximation to approximate the y-coordinate when x = 1.01.

Question 19 options:

0.996


1


1.004


Cannot be determined


1.388




The volume of an open-topped box with a square base is 245 cubic centimeters. Find the height, in centimeters, of the box that uses the least amount of material.



7.883 centimeters


6 centimeters


3.942 centimeters


3 centimeters


2 centimeters

Answer 1

x2 + sin(xy) + 3y2 = C
solve for dy/dx
2x+cos(xy)xdy/dx+6ydy/dx=0

dy = -2x/(cos(xy)x+6y) * dx

dy= -2*1/(cos(1*1) + 6) dx
but dx= .001
then dy= -.02/(.540+6)= -0.00305810398
so y= 1-dy= 0.996941896