Answer "true or false". a) If a×b •c=0,we can thus affirm that a,betc are collinear. b) 100 km/h north is a geometric representation of a vector in 2 . ________ ________ ________ ________ ________ ________ ________ ________ ________ c) We know that a = kb when a and b are orthogonal vectors. d) In the vector equation [x,y,z]=[x1,y1,z1] t[m1,m2,+m3], [x1,y1,z1]represents the position-vector of the line. e) In the analysis of three planes defined according to their Cartesian equation, the mixed product determines whether the planes intersect in a straight line. f) For any function, the average rate of change over the interval 0 < x < 2 equals the instantaneous rate of change at x = 2. g) To determine the derivative function of g(θ) = π sinθ , we must consider this as a product of functions and apply the rule. h) The expression f (b ) − f (a ) , makes it possible to establish the slope of the secant between two points. b−a i) For f(x)=32x 1, the derivative function is f'(x)=2x−23. j) If, at a critical point, the second derivative is positive, this critical point corresponds to a maximum.
Answer "true or false". a) If a×b •c=0,we can thus affirm that a,betc are collinear. b) 100 km/h north is a geometric representation of a vector in 2 . ________ ________ ________ ________ ________ ________ ________ ________ ________ c) We know that a = kb when a and b are orthogonal vectors. d) In the vector equation [x,y,z]=[x1,y1,z1] t[m1,m2,+m3], [x1,y1,z1]represents the position-vector of the line. e) In the analysis of three planes defined according to their Cartesian equation, the mixed product determines whether the planes intersect in a straight line. f) For any function, the average rate of change over the interval 0 < x < 2 equals the instantaneous rate of change at x = 2. g) To determine the derivative function of g(θ) = π sinθ , we must consider this as a product of functions and apply the rule. h) The expression f (b ) − f (a ) , makes it possible to establish the slope of the secant between two points. b−a i) For f(x)=32x 1, the derivative function is f'(x)=2x−23. j) If, at a critical point, the second derivative is positive, this critical point corresponds to a maximum.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Answer "true or false".
a) If a×b •c=0,we can thus affirm that a,betc are collinear.
b) 100 km/h north is a geometric representation of a vector in 2 .
________
________
________
________
________
________
________
________
________
c) We know that a = kb when a and b are orthogonal vectors . d) In the vector equation [x,y,z]=[x1,y1,z1] t[m1,m2,+m3],
[x1,y1,z1]represents the position-vector of the line.
e) In the analysis of three planes defined according to their Cartesian equation, the mixed product
determines whether the planes intersect in a straight line.
f) For any function, the average rate of change over the interval 0 < x < 2
equals the instantaneous rate of change at x = 2.
g) To determine the derivative function of g(θ) = π sinθ , we must
consider this as a product of functions and apply the rule.
h) The expression f (b ) − f (a ) , makes it possible to establish the slope of the secant between two points.
b−a
i) For f(x)=32x 1, the derivative function is f'(x)=2x−23.
j) If, at a critical point, the second derivative is positive, this critical point corresponds to a maximum.
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