For the following exercises, the given limit represents the derivative of a function y=f(x) at x=a. Find f(x) and a. limit as h approaches zero: ([3(2+h)^2 +2] - 14)/h

and the limit is 12

Step-by-step explanation:

we know that the derivative of the function f in x=a is the limit of this

as the expression is

we can say that

from the first equation we can identify a = 2 and then

to verify that we are correct, we can compute f(2)=3*4+2=14

f'(x)=6x

so f'(2)=12

we can estimate it from the fraction as well

so the limit is 12

77

step-by-step explanation:

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584