Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.Show that the formula 
obeys Condition II of the Principle of Mathematical Induction. That is, show that if the formula is true for some natural number k, it is also true for the next natural number 
. Then show that the formula is false for 
.
What will be an ideal response?
Assume the statement is true for some natural number k. Then
So the statement is true for 
.
However, when 
, the left side of the statement is , and the right side of the statement is
, so the formula is false for 
.
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Solve the problem.The radial flow field of an incompressible fluid is shown below. For which of the closed paths is the circulation not necessarily zero?
A. A, B, and C B. A and B only C. C only D. none of these
Provide an appropriate response.Define f(0,0) in such a way that extends f(x, y) = 
to be continuous at the origin.
A. No definition makes f(x, y) continuous at the origin. B. f(0, 0) = 2 C. f(0, 0) = 1 D. f(0, 0) = 0
Solve the problem.If f(x) = 6x2 - 5x and g(x) = 2x + 3, solve for f(x) = g(x)
A. 
B. 
C. 
D. 
Solve the system of equations using Cramer's rule.0.7x + 0.09y = 212x - y = -600
A. (800, 200) B. (200, 800) C. (200, -800) D. (2, 8)