Topic
Q:
Charlie is racing in a black car.
It is 12 noon.
He gets a 45 -mile headstart
from the starting line.
He then travels at a speed
of 70 miles per hour.
Write the equation for this scenario.
Q:
2. Sea \( f(x)=4 x^{2}-x+5 \) y \( g(x)=2 x^{3}-x \). Encuentra la derivada de \( h(x)=\frac{f(x)}{g(x)} \)
Q:
1. Hallar todas las raíces de \( P(x)=x^{3}-8 x^{2}+21 x-18 \) y factorizarlo.
b) Hallar el dominio y el conjunto solución de siguiente ecuación:
\[ \frac{P(x)}{x^{2}-36}=0 \]
\( (P(x) \) es el polinomio del ítem anterior \( ) \)
Q:
4. (10 points) Find all relative and absolute extrema of the function
\[ f(t)=\frac{1}{2} t^{4}+\frac{10}{3} t^{3} \]
with domain \( (-\infty,+\infty) \). Then the same function with domain \( [-2,+\infty) \)
Q:
A wooden artifact from an ancient tomb contains 40 percent of the carbon-14 that is present in living trees.
How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.)
years
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0^{+}}(6 x)^{\left(\frac{1}{7 \ln (3 x)}\right)} \]
Q:
c. \( \left(\frac{4}{9}-\frac{2}{7}\right)-\left(\frac{8}{7}-\frac{2}{9}\right)= \)
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 1}\left[\frac{2}{6 \ln (x)}-\frac{2}{6 x-6}\right] \]
Provide an exact answer.
Q:
1. Dadas las funciones \( f(x)=x^{3}+2 x-1 \) y \( g(x)=x^{2}+1 \), calcula la derivada de \( h(x) \)
\( \frac{f(x)}{g(x)} \).
Q:
Write the number in expanded form using exponents.
5. \( 74,271= \)
6. Number Sense Explain the difference between \( 4^{6} \) and \( 6^{4} \).
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