[10] 9. Use a graphing calculator to sketch the graph (on this paper) of the parametric curve 24t, y2 - 4t. Estimate the coordinates of the point where the graph crosses itself. Confirm your estimate algebraically, then find the equations of the two tangent lines to the graph at that point. [10] 9. Use a graphing calculator to sketch the graph (on this paper) of the parametric curve 24t, y2 - 4t. Estimate the coordinates of the point where the...
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction 2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction
The point (1,3) is on the graph of 22.73 + 6 - cz? = y2 + 24. Find the slope of the line tangent to the graph at that point: dy = da Enter your answer as a whole number (like-4, 0, or 253) or as a fraction (like 3/5, -7/2, or 1/3) or as DNE for Does Not Exist or undefined.
9 Geometry via calculus In this exercise you will see one way to use calculus to do grometry a) Here is one way to find the perpendicsler distance from a point to a line L (no caleulus yet) Let's say L has equation y-3r+2 and the point is (2.1) First, make a graph (picture) of the situation 2Now find an equation for the line AM through (2, 1) perpendicular to L (draw it first, of course). 3. Find the (coordinates...
MATH 241 S19 HOMEWORK 14 1. For each of theg, o dx (a) 4x3 + 7xy2 2Уз (b) x,5+1 xy + 1 2. For each of the following, find y': (a). xy sin(xy)-b) cosxy2)-y2+x 3. Find an equation of the line that is tangent to the graph of x2y2 4xy 12y at the point (2,) 4. Show that the graph of xy1 and the graph of x2-y2-1 intersect at right angles. 5. Given that x2 -y2 -1, show that y"...
16. Find all points on the circle x2 + y2 = 676 where the slope is 5/12 (x, y) = _______ (smaller y-value) (x, y) = _______ (larger y-value) 13.Find an equation of the tangent line to the graph at the given point. x2y2 - 9x2 - 4y2 = 0, (-4, -2√3) y = _______ 12. Find the slope of the tangent line to the graph at the given point. (4 - x)y2 = x3, (2, 2)
and C2 in the xy-planedefined by the parametric equations Consider trajectories on two curves C1:x=t?, y=t? - <t<«. C2: x = 3t, y=t?, - <t<mo. These two trajectories are known to *intersect* at exactly two points. The origin (0,0) is one of them. And there is another one, which we'll call P. Find Pand select the choice below which gives the slope of the tangent line to the first curve at the point P. Note that only ONE of the...
BREAKING NEWS Eyeballing Ellipses Evidence that Implicit Differentiation Works The graph of x2 -xy y2 = 4 is a tilted ellipse, as shown below. Sketch the approximate tangent lines on the ellipse where the slopes of the tangent lines are (a) zero and (b) undefined by "eyeballing". Label the coordinates with your best estimate to two decimal places. Then, use implicit differentiation to determine the exact values of the coordinates. Express your answers as proper square root ratios. Use a...
please answer the following parts. thank you in advance Let's consider the problem that has given rise to the branch of calculus called differential calculus: the tangent problem. This problem relates to finding the slope of the tangent line to a curve at a given point. To understand how this is done we are going to consider the point (0,0) on the graph of-snx. (5) 1. On graph paper, sketch the graph of y-sin and draw a tangent line at...
please answer all the following parts neatly. thank you Let's consider the problem that has given rise to the branch of calculus called differential calculus: the tangent problem. This problem relates to finding the slope of the tangent line to a curve at a given point. To understand how this is done we are going to consider the point (0,0) on the graph of f)-sinx (5) . On graph paper, sketch the graph of -sinx and draw a tangent line...