1. Say that we are attempting to evaluate sin ((x - 1)(y-2)) (x,y)+(1,2) (x - 1)2...
If sin x = and sin y = 13,0<x< 2,39 < y < 2., evaluate tan (x + y)
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
5)Evaluate f (x2-y)dr + (y2 +x)dy along a) a straight line from (0.1) to (1,2), b) straight lines from (0,1) to (1,1) and then from (1,1) to (1,2), c) the parabola z t,y 1
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + cos x y sin(cos x) y= sec(1 +x2) x cos y + sin 2y xy Use an Implicit Differentiation] 3. Find y" if x, y,6-1. [Use Implicit Differentiation] 4. Find an equation of the tangent to the curve at the given point. 121 12+ 1 [Use Implicit Differentiation] 4. Find the points on the ellipse x2 + tangent line has...
4. We have n statistical units. For unit i, we have (x; yi), for i 1,2,...,n. We used the least squares line to obtain the estimated regression line bobi . (a) Show that the centroid (z, y) is a point on the least squares line, where x-(1/n) Σ-Χί and у-(1/ n) Σ|-1 yi. (Hint: Evaluate the line at x x.) (b) In the suggested exercises, we showed that e,-0 and where e is the ith residual, that is e -y...
Let f(x, y) = (2x ^2y) /(x^4 + y^2) . We will investigate limiting behaviour of this function as (x, y) approaches (0,0). (a) Show that if we approach origin along any line that passes through the origin, f approaches to 0. (b) Approach the origin along the curve y = x 2 , what does f approach to? (c) Does f have limit at the origin? (d) What is the conclusion? Comment on the result.
Problem 11. Evaluate the given integral. (1) S (x -sin x)dr. (2) Si Vtct (3) / tan seczdz ANALYSIS Problem 12. Find the equation of the line whic c?y2 + 4 = 0 at (1,2) Find the equation of the line which is tangent to the graph of ty - Problem 15. Compute lim +6+ f(x) and lim,+-1-f(x) for f(x) = 7 y = -1, a horizontal asymptote of f? demonstrate. . Is 10 ANALYSIS 16.1 by finding a suitable...
Practice: Plot x vs y when y sin(x), y cosx), y sin (2"x), and y-2 sin(x) when x-1:0.1:10. Use 2 by 2 subplot, sin(x) is in location 1, cos(x) is in location 2, sin(2x) is in location 3 and 2 sin(x) is in location 4 The plot should have: (1) x labe|-"х value", y label = 'y value', legend 'y=sin(x)',' y-cos(x)',' y-sin (2*x)', "y-y-2*sin(x), and title = "X Vs. y, under Font Name of Times New Roman, and Font Size...
2x+5xy* 1) Let f(x,y) = *3+x3y2 Which among the following is true about limf(x,y)? (x,y)--(0,0) a. By using the two path test we can deduce that the limit does not exist b. By using the two path test we can deduce that the limit exists c. The limit is 2 d. None of the above O a. O b. O c. O d. 2) Let f(x,y) Vx+1-y+1 xy Then lim f(x,y) (xy)+(0,0) a. is 0 b.is c. is 1 d....
force field: find the work done by F in moving object from (0,1) to (1,2) along the path from x=0 to x=1 We were unable to transcribe this imagey = 1 + sin(π·r/2)