For 20 points, 5 stars, and a thanks, can some one answer these 5 questions about percent increase and decrease?
2 answers:
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Answer:
(a) k'(0) = f'(0)g(0) + f(0)g'(0)
(b) m'(5) =
Step-by-step explanation:
(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use <u>product rule</u>,i.e.,
this will give <em>k'(x)=f'(x)g(x) + f(x)g'(x)</em>
on substituting the value x=0, we will get the value of k'(0)
{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}
(b) m(x) is a function of two functions f(x) and g(x) [ ]. Since m(x) has a function g(x) in the denominator so we need to use <u>division rule</u> to differentiate m(x). Division rule is as follows :
this will give <em></em>
on substituting the value x=5, we will get the value of m'(5).
{for expressing the value in terms of numbers first we need to know the value of f(5), g(5), f'(5) and g'(5) in terms of numbers}
{NOTE : in m(x), g(x) ≠ 0 for all x in domain to make m(x) defined and even m'(x) }
{ NOTE : }
we are given
system of equations
First equation is
Second equation is
now, we can find augmented matrix
now, we can change it into reduced row echelon form
step-1: multiply the 1st row by 1/3
step-2:add -3 times the 1st row to the 2nd row
step-3:multiply the 2nd row by 1/4
step-4: add 2/3 times the 2nd row to the 1st row
so, we get
Answer is (5,-8)
