Find the linear approximation of the function
f(x) = sqrt of (1 − x) at a = 0. use l(x) to approximate the numbers sqrt of 0.9 and sqrt of 0.99.

1−x−−−−√≈−12x+1

0.9−−−√=1−0.1−−−−−−√≈−12(0.1)+1

To simplify:

−1/2⋅1/100+1=−1/2⋅1/100+200/200=200−1/200=199/200 or =.995

So yes for sqrt (.99), that is a good approximation.

To write linear approximations:

Our curve should be  y=f(x) and substitute x=a for the numbers m

 Our formula for the linear equation is  y=mx+b

So subtsitute

y′=f′(x)

y=f′(a)x+b

Then find the  y-intercept, which is  b.

Given:  (a, f(a))= point of the line

Then substitute, that would be

f(a)=f′(a)⋅a+b

f(a)−f′(a)⋅a=b

So the tangent line to y=f(x) at x=a

Or the equation we will use for linear approximations is:

y=f′(a)x+f(a)−f′(a)⋅a

y=f′(a)⋅(x−a)+f(a)

well if he bought them at 5 cedis each sold them at 7 cedis each then he would make a profit of 2 cedis of each book. if in total he made 150 cedis profit that means he sold 75 books. he lost 12 books at the start so that means he originally bought a total of 82 books.

step-by-step explanation: