calculus

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

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  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

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    2. 👎 1

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