Explain a. How close does the curve yx come to the point (Hint: If the square...
what is the answer?
(1 point) Finding the length of a curve. Arc length for y = f(x). Let f(x) be a smooth function over the interval [a, b]. The arc length of the portion of the graph of f(x) from the point (a, f(a)) to the point (b, f(b)) is given by V1 + [f'(x) dx Part 1. Let f(x) = 2 ln(x) - Setup the integral that will give the arc length of the graph of f(x) over...
RSS3 points 12. Find the point on the curve y=Vx that is a minimum distance from the point (4,0). Report your answer as an ordered pair in the format (x, y) and round each coordinate to the nearest tenth. 13. Consider all lines in the xy-plane that pass through both the origin and a point (x, y) on the graph of the parabola y = x^2 - x + 16 for (1,8). The figure below shows one such line and...
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1, 2). Find the gradient of f at the point P and draw the gradient vector on the level curve (ii) Draw the graph of f showing the level curve in (i) on the graph (iii) Explain why the function f admits a global minimum over the rectangle 0 x 2, y 1. Determine the minimum value and...
(4) LaGrange Multipliers Minimize the square of the distance from y = x^2 to the point (0,3). (4a) Let g(x,y)=y=+ = 0 and state gx, gy. (4b) Let + =f(x,y) = x +(-3) and state fx, fy. (4c) State and solve a system of 3 equations for x,y and 2 (40) What is the minimum value of d?
(4) LaGrange Multipliers Minimize the square of the distance from y = x^2 to the point (0,3). (4a) Let g(x,y) = y - x = 0 and state gx, gy. (4b) Let : =f(x,y) = x +(y - 3) and state fx, fy. (40) State and solve a system of 3 equations for x,y and 2. (40) What is the minimum value of d?
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...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
3 8 16 (0 complete) This Q Plot each point and form the triangle ABC. Show that the triangle ABC is a right triangle. Find its area. A (-2,11); B (5,7); C ( 1,0) Choose the correct graph below that shows points A, B, C, and triangle ABC. O A. O B. O C. OD. -14 14 Ha Show that the triangle ABC is a right triangle. Select the correct choice below and fill in the answer boxes to complete...
In a special race, the goal is to get from point A on a pool’s
deck to point B in the water, where there is a buoy, in the
shortest amount of time if one is allowed to run or swim.
(a) Find an expression for the time an athlete takes to get from
A to B, if she is running a distance x with the constant speed vR
and then swimming from S to B with the constant speed...
QUESTION 1 a. The sum of eight and a certain number is multiplied by six gives fifty four. What is the number (3 marks) b. It was observed that Duke Street intersect Habour Street at right angle adjacent the Bank of Nova Scotia down town, Kingston which for most part are straight roads. If Harbour Street and Duke Street are represented by equations x+2y=9A2x-y=-2 respectively and two cars are travelling the same distance and speed. At what point will they...