Writing a Vector in Different Forms In Exercises 9-16. the initial and terminal points of a vector v are given, (a) Sketch the given directed line segment, (b) Write the vector in component form. (c) Write the vector as the linear combination of the standard unit vectors i and j. (d) Sketch the vector with its initial point at the origin. Initial Point Terminal Point ( 0.12 , 0.60 ) ( 0.84 , 1.25 )
Writing a Vector in Different Forms In Exercises 9-16. the initial and terminal points of a vector v are given, (a) Sketch the given directed line segment, (b) Write the vector in component form. (c) Write the vector as the linear combination of the standard unit vectors i and j. (d) Sketch the vector with its initial point at the origin. Initial Point Terminal Point ( 0.12 , 0.60 ) ( 0.84 , 1.25 )
Solution Summary: The author explains that the required graph is langle 0.72,0.65rangle.
Writing a Vector in Different Forms In Exercises 9-16. the initial and terminal points of a vector v are given, (a) Sketch the given directed line segment, (b) Write the vector in component form. (c) Write the vector as the linear combination of the standard unit vectors i and j. (d) Sketch the vector with its initial point at the origin.
Initial Point Terminal Point
(
0.12
,
0.60
)
(
0.84
,
1.25
)
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
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