You can check that the limit comes in an undefined form:
In these cases, we can use de l'Hospital rule, and evaluate the limit of the ratio of the derivatives. We have:
and
So, we have
Answer:
a^6
Step-by-step explanation:
when multiplying exponents, add the exponents together. you can distribute to prove it, a^2 is a•a, a^3 is a•a•a so by bringing it together you get a•(a•a)•(a•a•a) which gets a 6 times or a^6
To solve this problem we can find the area of the whole rectangle, then find the area of the smaller white rectangle inside the whole rectangle. Lastly, we can subtract the area of the smaller rectangle from the area of the whole rectangle which leaves us with the area of the shaded region.
Area of whole rectangle = length x width
= (3x + 6) (2x + 4)
= 6x squared + 24x + 24
Area of small rectangle = length x width
= (x-3) (x - 1)
= x squared - 4x + 3
Area of shaded region = area of whole rectangle - area of small rectangle
= 6x squared + 24x + 24 - x squared + 4x - 3
= 5x squared + 28x + 21
Answer:
Step-by-step explanation:
Remember that our original exponential formula was y = a b x. You will notice that in these new growth and decay functions, the b value (growth factor) has been replaced either by (1 + r) or by (1 - r). The growth "rate" (r) is determined as b = 1 + r.
An exponential function of a^x (a>0) is always ln(a)*a^x, as a^x can be rewritten in e^(ln(a)*x). By deriving, the term (ln(a)) gets multiplied with a^x. The derivative shows, that the rate of change is similiar to the function itself. For 0<a<1, ln(a) becomes negative and so is the rate of change.
Linear models are used when a phenomenon is changing at a constant rate, and exponential models are used when a phenomenon is changing in a way that is quick at first, then more slowly, or slow at first and then more quickly.
Answer: the circle wth 3 covered goes in 1/2 and the rectangle and the other circle go in 3/5 the small square with 2 covered goes in other and the long line of squares goes in other
Step-by-step explanation:
