Let f(x, y,z)=x+yz and let C be the line segment from P=(0,0,0) to (6,3,1). (a) Calculate f(c(t)) and ds=∥c′(t)∥dt for the parametrization c(t)=(6t,3t,1t) for 0≤t≤1. (b) Evaluate ∫Cf(x, y,z)ds.

h df tyjgtyj ttd y ytkgfty ty

step-by-step explanation:

tyty jry j y yj yttj yhgtyj y ghyj ytthj

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

2

step-by-step explanation: