Evaluate the line integral ∫c(−𝑥 + 𝑦 + 𝑧) 𝑑𝑥 + (𝑥 + 𝑦 − 𝑧) 𝑑𝑦 + (𝑥 − 𝑦 + 𝑧) 𝑑𝑧 where C is the line segment from the point 𝑃(−1, 2, 3) to 𝑄(3, −2, 1).
A parametric curve is given by the equations
𝑥 = 𝑡 − 𝑠𝑖𝑛𝑡 and 𝑦 = 1 − 𝑐𝑜𝑠𝑡
Find dy/dx and d^2y/dx^2 at the point (𝜋,2).
Determine if the two vectors are skew lines or if they intersect each other. !D = h2;3;1i+d h5;3;6i and −!F = h−5;−3;−5i+ f h15;3;−3i
Show that f(x)=1/x does not have extreme values in interval (0,1).
What is the Cartesian form of