Multiply 12 by 4%, or 4/100, and 4/100 simplifies to 1/25. 12/1 x 1/25 = (12 x 1)/(1 x 25) = 12/25, which equals 0.48. So, the smallest frog is 0.48 inches long, but can be rounded to 0.5 inches long.
9514 1404 393
Answer:
- 2 complex roots
- 2 positive real roots
- 0 negative real roots
Step-by-step explanation:
The signs of the terms are + - - +. There are two sign changes, so 0 or 2 positive real roots.
Negating the signs of the odd-degree terms, the signs are + + + +. There are no sign changes, so 0 negative real roots.
For x=0, the value of the quartic is +3. For x=1, the value is -3, so we know there are 2 positive real roots, one of which lies in the interval (0, 1).
The 4th-degree polynomial equation must have 4 roots, so the other two must be complex.
- 2 complex roots
- 2 positive real roots
- 0 negative real roots
_____
The roots are approximately 0.489999841592, 2.06573034434, −0.777865092969 ± 1.53582061225i
Answer:
General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Constant]:
Limit Rule [Variable Direct Substitution]:
Limit Property [Addition/Subtraction]:
L'Hopital's Rule
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Addition/Subtraction]:
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
We are given the following limit:
Let's substitute in <em>x</em> = -2 using the limit rule:
Evaluating this, we arrive at an indeterminate form:
Since we have an indeterminate form, let's use L'Hopital's Rule. Differentiate both the numerator and denominator respectively:
Substitute in <em>x</em> = -2 using the limit rule:
Evaluating this, we get:
And we have our answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits