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- Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law, which shows the relationship among volume V, pressure p, and temperature T for a fixed amount 1 mole of a gas. But chemists believe that in many situations, the van der Waals equation gives more accurate results. If we measure temperature T in kelvins, volume V in liters, and pressure p in atmosphere 1 atm is the pressure exerted by the atmosphere at sea level, then the relationship for carbon dioxide is given by p=0.082TV0.0433.592V2atm What volume does this equation predict for 1 mole of carbon dioxide at 500 kelvins and 100 atm?Suggestion: Consider volumes ranging from 0.1 to 1 liter.(Differentiation) 6.1.7.3) Finding equation of normal line to the curve at (2,1) ( Ans. x + 2y - 4 = 0 )A straight line perpendicular to and passing through the point of tangency of the tangent line is called the normal to the curve. Find an equation of the tangent line and the normal to the curve y = x3 − 3x + 3 at the point (2, 5). (Let x be the independent variable and y be the dependent variable.) tangent liney= 24x−45 normal liney=
- Find the equations of the tangent line and normal lines to the graph of the function f(x)=−2sin x at x=π/2 a) Tangent line: ? b) Normal line?A straight line perpendicular to and passing through the point of tangency of the tangent line is called the normal to the curve. Find an equation of the tangent line and the normal to the curve y = x3 − 3x + 2 at the point (3, 20). (Let x be the independent variable and y be the dependent variable.)how do you find the (a). equation of the scant line through the points wehre x has the given values, and (b). the equation of the tangent line when x has the first value. f(x) = x2 + 2x ; x = 3, x = 5.
- 5) Find the equation of a tangent line to the curve y= 2x^3 - 3x^2 - 10x + 1 which is perpendicular to the line x + 2y - 6=0. Topic: Tangent Lines, Normal Lines, and Rates of Change Thank you for the answer ?Determine the equation for tangent and normal at the point with x -coordinate 1 on the curvey = 2 x3− 2 x2− 4 x − 2 (a) The equation of the tangent of the form y = kx + m (b)The equation of normal of the form y = kx + mequation of the tangent line to the curve at the given point. y = 2 + x3 , (−1, 1)
- A. Find the slope of the curve y=x2-2x-3 at the point P(2,-3) by finding the limiting value of the slope of the secant lines through point P. B. Find an equation of the tangent line to the curve at P(2,-3)Find the equation of the tangent line at point (2,2)for the function x^2+y^2=4xy Find the normal line1.Find the lines that are tangent and normal to the curve at the given point. x2y2=36 (-3,2) The line tangent to the curve x2y2=36 at (-3,2) is y= 2. Find the lines that are tangent and normal to the curve at the given point. y=6 sin(pi*x+y), (-1, 0) The line tangent to the curve y=6 sin(pi*x+y) at (-1, 0) is y=??