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Chapter 1 Solutions
Calculus (MindTap Course List)
- Decide whether each limit exists. If a limit exists, estimate its value. 11. (a) lim f(x) x-3 f(x) ↑ 4 3- 2+ (b) lim f(x) x―0 -2 0 X 1234arrow_forwardDetermine whether the lines L₁ (t) = (-2,3, −1)t + (0,2,-3) and L2 p(s) = (2, −3, 1)s + (-10, 17, -8) intersect. If they do, find the point of intersection.arrow_forwardConvert the line given by the parametric equations y(t) Enter the symmetric equations in alphabetic order. (x(t) = -4+6t = 3-t (z(t) = 5-7t to symmetric equations.arrow_forward
- Find the point at which the line (t) = (4, -5,-4)+t(-2, -1,5) intersects the xy plane.arrow_forwardFind the distance from the point (-9, -3, 0) to the line ä(t) = (−4, 1, −1)t + (0, 1, −3) .arrow_forward1 Find a vector parallel to the line defined by the parametric equations (x(t) = -2t y(t) == 1- 9t z(t) = -1-t Additionally, find a point on the line.arrow_forward
- Find the (perpendicular) distance from the line given by the parametric equations (x(t) = 5+9t y(t) = 7t = 2-9t z(t) to the point (-1, 1, −3).arrow_forwardLet ä(t) = (3,-2,-5)t + (7,−1, 2) and (u) = (5,0, 3)u + (−3,−9,3). Find the acute angle (in degrees) between the lines:arrow_forwardA tank initially contains 50 gal of pure water. Brine containing 3 lb of salt per gallon enters the tank at 2 gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min. Thus, the tank is empty after exactly 50 min. (a) Find the amount of salt in the tank after t minutes. (b) What is the maximum amount of salt ever in the tank?arrow_forward
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