The independent variable x is plotted along the x-axis (a horizontal line), and the dependent variable y is plotted along the y-axis (a vertical line). When the graph of a relation between x and y is plotted in the x-y plane, the relation is a function if a vertical line always ...
Find all values of t at which the parametric curve, f(t), has a horizontal or vertical tangent line. x = 10 \cdot \sin (2t), \; y = 60 \cdot \cos (2t) \; (0 \leq t \leq \pi) Find {d^2y} / {dx^2} for the parametric curve x = sec ...
(1)Find dy/dx and d^2y/dx^2. (2)Find the equation of the tangent line at the point where θ=π/6. (3)Find all points of horizontal tangency. (4)Determine where the curve is concave upward or concave downward. (5)Find the length of one are of the curve. 相关知识点: 试题...
Answer to: Find the parametric equations for the tangent line to the curve x = t^4 - 1, y = t^3 + 1, z = t^3 at the point (15, 9, 8). Use the...
1. Use the formula for the slope of the tangent line to find dy/dx for the curve c(t) = (t^-1 - 5t, 9t^3) at the point t = -1. 2. Find the points on the parametric curve c(t) = (3t^2 - 2t. t^3 Find the points on the p...
1. 在模型树中,选择“基准点 ID 1690”(Datum Point id 1690) ,然后单击“通过 点的曲线”(Curve through Points) 。 2. 在操控板中单击“使用线”(Use Line) ,从样条切换为直线。 3. 单击“预览特征”(Preview Feature) 。 图 2 4. 单击“恢复特征”(Resume Feature) 。 5. 单击“倒圆角曲线”(...
1. 单击“基准”(Datum) 组下拉菜单并选择“曲线”(Curve) 。 2. 在模型树中,选择“基准点标识 1690”(Datum Point id 1690)。 3. 在操控板中单击“使用线”(Use Line) ,从样条切换为直线。 4. 单击“预览特征”(Preview Feature) 。 Enlarge Image 图 3 5. 单击“恢复特征”(Resume Feature) 。 6...
For what values of t is the tangent line to the parametric curves x = t^3 - t, y = t^2 - 1 horizontal?What is an integral curve?Describe and plot the curve given by parametric description. r(t) = t_x (2 cos^2 t) + t_y (2 sin^2 t)....
Find parametric equations of the tangent line to the curve x = 4t + 8, y = (1/6)t^6, z = 3/(1 + t^2) at the point t = 2. Find parametric equations for the tangent line at the point (\cos(4\pi/6), \sin(4\pi/6) , 4...
a. Graph the curve. b. Obtain the Cartesian equation of the curve by eliminating the parameter. Sketch the parametric curve x = 5-3t, y =2+t; \quad -1 \leq t \leq 3 . Find a new equation by eliminating the parameter. Find parametric equati...