tailieunhanh - Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 71

Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 71. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | A Brief Introduction to Vectors 681 c How far has the object traveled horizontally when it hits the ground In other words what is the horizontal component of its displacement vector d When the object hits the ground how far is it from where it was launched In other words what is the length of its displacement vector 10. Force A has a horizontal component of 3 pounds and a vertical component of 4 pounds. Force B has a horizontal component of 5 pounds and a vertical component of 12 pounds. a What is the strength of force A What angle does this force vector make with the horizontal Give a numerical approximation in degrees. b What is the strength of force B What angle does this force vector make with the horizontal Give a numerical approximation in degrees. c What is the component of force A in the direction of force B 11. There s a 10-mile-per-hour wind but a bicyclist calculates that its component in his direction of motion is only 9 miles per hour. What is the angle between the velocity vector of the wind and that of the bicyclist 12. Due to the scampering of a goat a rock has been dislodged from a mountain and is sliding down an incline making a 70 angle with level ground. The weight of the rock exerts a downward force of 3 pounds. What is the component of this force in the direction of motion of the rock rock goat 3 lbs downward 70 C H Differentiation of Trigonometric Functions INVESTIGATING THE DERIVATIVE OF SIN X GRAPHICALLY NUMERICALLY AND USING PHYSICAL INTUITION Graphical Analysis Figure presents the graphs of f x sin x g x cos x and sketches qualitatively done of their derivative functions. Where the function is increasing its derivative is positive or zero where the function is decreasing its derivative is negative or zero. Where the function is concave up its derivative is increasing where the function is concave down its derivative is decreasing. Sine and cosine are periodic with period 2n. Similarly their derivatives must be periodic with