Calculus 1

Calculus 1, Lab #7 Implicit Plots and Tangent Lines The goals of this lab is to 1. get you to practice finding Implicit Derivatives, 2. demonstrate plotting of curves defined by equations in Matlab, and 3. verify that you have correctly found the implicit derivative at a point for those curves by plotting the curve, the point and the tangent line. As always, you must include a header as in previous labs. Also, you must show your TA your by-hand work to get full credit for each of the three problems at the end. You do not need to include that by-hand work in the Live Script you submit. . Example: In MATLAB, plot the tangent line to the circle x2 + y2 = 1 at the point V2 V2 (23) Steps 1. By hand, find dy/dx. (In this example, confirm that dy/dx = -x/y). 2. Evaluate the derivative, calling it ‘m’at the given point in Matlab a. xl=sqrt(2)/2; yl=sqrt(2)/2; b. m = -xl/y1 3. Enter the equation and tangent line into Matlab. Note that an “equation” is an expression that would be equal to zero. a. syms X Y b. eqn1 = x^2 + y^2-1 c. tanlinel = m* (x-x1)+y1 у 4. Plot the curve, point and tangent line in Matlab. a. ezplot (eqni) b. hold on c. scatter([xl],[y1]) d. ezplot(tanlinel) e. title( [ʻYour Name Goes Here’, date]) At this point you should have a plot of a circle with a tangent line at the specified point. 5. (Optional) Verify your by-hand derivative using MATLAB to find the derivative of the original equation and solving for dy/dx. a. syms x y(x) dy_dx b. eqn1ALT = x^2 + y(x)^2 -1 c. DerofEquation diff(eqn1ALT,x) d. DerofEquation=subs (DerofEquation, diff(y(x),x),dy_ dx) e. dy_dx=solve (DerofEquation, dy_dx) = Putting it All Together Repeat Steps 1 to 4 for the following curves and respective points. Be sure to show Step 1, the by-hand work, to your TA before you continue. Submit Steps 2 to 4 in your LiveScript. 1. x4 + 2x2y2 – 4x2y – 4×2 + y4 – 4y3 = 0 at the point(** + 1,73 +3) 2. sin(x+y) = y² cos(x) at the point (0,0). V3 V3 3. y* = y² – x?at the point 4 2
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