The parametric equation of a curve is x=\sin t and y= \frac{2}{\sin t}. Find t, when the tangent has slope = -1. Find the parametric equations for the tangent line to the curve x = t^2 - 1, y = t^2 + 1, z = t^3
{/eq} To find the slope of a tangent line, we treat it as parametric equation, {eq}x=r(\theta)\cos \theta,\, y=r(\theta) \sin \theta {/eq} and have: {eq}\dfrac{dy}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}=\dfrac{r'\sin \theta...
Temperature variation along the line \(x_{2} = 0.5\) for Ra = 100,000 and different M. Full size image Conclusions Impact of the two nearby current carrying wires on the momentum and temperature behavior in the flow (driven by external pressure gradient) inside a vertical duct has be...
1(b). The effect of the radius of influence area increases in line with increases to the angle of tapering. Moreover, it was found that the convex heave on the pile–ground interface had narrowed and decreased in the tapered piles. The reason for this mechanism is due to an increase in...
In the calculation of R all phase difference values are first transformed to two-dimensional unit vectors: ri=(cosϕisinϕi) and then averaged over all data samples i, while ϕ¯ was obtained by using the four quadrant inverse tangent function on R [40]. Table 3. Statistical ...
Find the points where the tangent to the parametric curve x = 8e^{2t}, \quad y = t^2e^{2t} are horizontal or vertical. Consider the polar curve r=1+sin\theta. (a) Find the equation of the tangent line to this polar curve at \theta =0. (b...
Find the points on the given parametric curve where the tangent line is horizontal or vertical x = 1 + 3 c o s t , y = 2 2 s i n t , t R Find the points where the tangent to the parametric curve x = 8e^{2t}, \quad y = t^2e^{2t} are horizontal...
Find the tangent line to the curve r=1-\sin \theta at the point when \theta =\frac{\pi}{6} Find the points on the given parametric curve where the tangent line is horizontal or vertical x = 1 + 3 c o s t , y ...
If the parametric curve x = f (t), y = g (t) satisfies g (1) = 0, then it has a horizontal tangent w Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or ...
For what values of x, does the graph of f(x) = x + 2\sin x have a horizontal tangent? Determine whether the graph is that of a function by using the vertical-Iine test. If it is, use the graph to find: Which of the following functions has a graph th...