In April 2024
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Prove that a space curve is a helix if and only if the ratio of the curvature to the torsion is constant at a points
for the curve x=a(3u-u³), y=3au², z=a(3u+u³) prove that k=t
Use the Bisection method to find solutions accurate to within 10^−5 for the following problems. a. x − 2^−x = 0 for 0 ≤ x ≤ 1
b. ex − x^2 + 3x − 2 = 0 for 0 ≤ x ≤ 1
c. 2x cos(2x) − (x + 1)^2 = 0 for −3 ≤ x ≤ −2 and −1 ≤ x ≤ 0 d. x cos x − 2x^2 + 3x − 1 = 0 for 0.2 ≤ x ≤ 0.3 and 1.2 ≤ x ≤ 1.3
Show that {𝑥} ⊆ ℝ is connected
Show that {𝑥} ⊆ ℝ is connected.
Find the angle nearest to the whole number between the surfaces x2+y2+z2=9 and z=x2+y2-3 at the point (2, -1, 2).
Prove that a space curve is a helix if and only if the ratio of the curvature to the torsion is constant at a points
if P is any point on the circle C in the XY plane of a radius a>0 and centre(0,a ) ,let the straight line through origin and P intersect the line y=2a at Q and let the line trough P parallel to the Xaxis intersect the line through Q parallel to the Y axis at R.as P moves around C , R trace out a curve find its paramatrisation and its cartesian equation
sketch the astroid in curves also calculate its tangent vector at each point .at which point is the tangent vector zero:
(i) γ(t) = (cos^2 t, sin^2 t)
(ii) γ(t) = (e^t, t^2)
find the largest area of the isosceles triangle OAB as shown in the figure below . the point a is on the the x-axis while the point b lies on the curve y=49-x² in the first quadrant( use second derivative method)
#339914 on Dec 2023