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Find the slope of the curve below at the given points. Sketch the curve along with its tangent lines at these points. r= - 4+4 cos 0; O= The slope at the point o = 5 is (Simplify your answer.) The slope at the point 0 = (Simplify your answer.) is Identify the curve r= - 4 + 4 cos 0. OA. OB. OC. Give a geometric description of the set of points in space whose coordinates satisfy the given...
3. [10] (quadrifolium) Let (a2 + y2) = (2 -)2 be a curve. Find the points on the curve where the normal line is parallel to y 0. re2y, find the normal line at 4. [4] Let (1,0). [0, 10] with f(0) f(10) 0 and 5. 5 Let f(a) be continuous and differentiable on f(5) 4. Mark TRUE or FALSE for the following statements and JUSTIFY. (No points will be given without the correct justification) (A) There is some c...
Differentiate implicitly to find dy / dx. Then find the slope of the curve at the given point. x?y2 = 36, (3,-2) The slope of the curve at (3,-2) is (Simplify your answer.)
Differentiate implicitly to find dy / dx. Then find the slope of the curve at the given point. x?y2 = 36, (3,-2) The slope of the curve at (3,-2) is (Simplify your answer.)
(1 point) Find the area of the surface obtained by rotating the curve 4x = y2 + 8 about x-axis from x = 2 to x = 4. Area:
16. Find all points on the circle x2 + y2 = 676 where the slope is 5/12 (x, y) = _______ (smaller y-value) (x, y) = _______ (larger y-value) 13.Find an equation of the tangent line to the graph at the given point. x2y2 - 9x2 - 4y2 = 0, (-4, -2√3) y = _______ 12. Find the slope of the tangent line to the graph at the given point. (4 - x)y2 = x3, (2, 2)
No 3
putin uhd e integral lound a r the val- 0 VIIl, 81. EXERCISES Compute the curve integrals of the vector field over the indicated curves. (x,y)=(x2-2xy,y2-2xy) along the, parabola y=x2 from (-2,4) to 2. 0x, y, xz - y) over the line segment from (0,0, 0) to (1, 2, 4), 3, Let r (x2 y2)1/2 Let F(X)-X. Find the integral of F over the circle of radius 2, taken in counterclock wise direction. 4. Let C be a...
A curve is such that =-4x. The curve has a maximum point at (2, 12). (i) Find the equation of the curve. [6] A point P moves along the curve in such a way that the x-coordinate is increasing at 0.05 units per second. (ii) Find the rate at which the y-coordinate is changing when x = 3, stating whether the y-coordinate is increasing or decreasing. 127
Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 6sin(θ) θ = π/3 Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 4 - sin(θ) θ = π/4 Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 9/θ...
1&2
1. Find dy/dx for the curve r + xy + y2 = 3. 2. Use local linearization to estimate V29. Leave your answer as a simplified fraction.