MATH 205 Quiz: MATH 205 Louisville Quiz 4 150220

MATH 155 Technical Calculus Homework Indefinite Integrals Name Integrate each of the given expressions. Show all work for any credit. Each prob worth 3 points lem is 6, Find y in terms of x foray = 3x2 + 4-1, curve passes through (-1,3) dx

(1) Use implicit differentiation to find dy/dx if xy = sin x + sin y (2) Suppose 6x2 +3xy+ 2y^2 + 17y - 6 = 0. (a) Use implicit differentiation to find the derivative (b) Find an equation for the line tangent to the graph at (x, y) = (-1,0). (3) Find the equation of the tangent to the curve given by 2(x - y^2)^2 = 25(x^2 - y^2) at the point (3,1). (4) Find dy/dx and d^2y/dx^2 by Implicit differentiation for the curve given by x^2 + xy - y^2 = 4 Express the second derivative in terms of x and y. (5) The curve with equation x^2 + xy + y^2 = 7 has two x-intercept. Find the equation of the lines tangent to the curve at those two intercepts.

Use the chain rule to find the derivative of at x = 1. Enter just an Integer. Compute dy/dx· using the chain rule where y = u 2 and u = 3x = 4. Enter your answer as just a polynomial in x in standard form (no label). Compute dy/dx using the chain rule where y = u 2/u 2 + 1- and u = at x = 1 Enter just a reduced fraction. Use implicit differentiation to determine dy/dx where 4x 3 + 4xy + y = 8. Find the equation of the tangent line to the graph of x 2 + y 2·= 1 at the point [1/2, /2] Use implicit differentiation to determine dy/dx where xy + 10 = x 2.