In (x-2)* In sketching y O no horizontal asymptote O y = 0 and y = 3 O None of the choices O y = 3 O y = 0 determine the horizontal asymptote. "
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- Sketch a graph of x=-3+2cos(t), y= -2+2sin(t), 0< t < 2piFind all points (x, y) on the graph of g(x) = 1/3 x3 - 3/2 x2 + 1 withtangent lines parallel to the line 8x - 2y = 1.Find the values of constants a, b, and c such that the graph of y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection point at (1, 11).
- Assume that dx1/dt= x1(10-2x1-x2) dx2/dt= x2(10-x1-2x2) a) Graph the zero isoclines. b) Show that (10/3, 10/3) is an equilibrium, and use the analytical approach to determine its stability.7. Determine values of a, b, and c such that the graph of y = ax³ +bx² + c has a local extremum at (2, 11) and a point of inflection at (1, 5).With y=c1.x2+k curves and curves x2+2.y2-y= c2 intersect perpendicularly. Where C1 and C2 are arbitrary constants, So what is the value of k?
- find constants a and b so that the minimum for the parabola f(x)=x2+ax+b is at the point (6,7)Find a quadratic function associated with vertex (h, k) = (1, 0) and point(x, y) = (–3, 4) that the parabola passes through. a .f(x)= 1/4 x^2+1 b. f (x)1/4 (x-1)^2 c.f(x)= 1/4 (x+3)^2 +4 d. f(x)= - 1/4 (x -1) ^2- Find by integration the area of the triangle having vertices at (5, 1), (1, 3), and (-1,-2). - Find by integration the area of the triangle having vertices at (3, 4), (2, 0), and (0, 1). - Find the area of the region bounded by the curve x³ x² + 2xy - y² = 0 and the line x = 4. (HINT: Solve the cubic equation for y in terms of x, and express y as two functions of x.) Find the area of the region bounded by the three curves y = x², x = y³, and x + y = 2. Find the area of the region bounded by the three curves y = x², y = 8 - x², and 4x - y + 12 = 0.