Topic
Q:
\( \int ( 2 \pi \sin w x + 2 ^ { x } ( 2 + \frac { 3 } { 2 ^ { x } } ) - \frac { 1 } { x ^ { 2 } } - \frac { \cos e c x } { \tan x } + e x ) d x \)
Q:
Question
For the equation given below, one could use Newton's method as a way to approximate the solution. Find Newton's formula
as \( x_{n+1}=F\left(x_{n}\right) \) that would enable you to do so.
\[ \ln (x)+1=10 x \]
Provide your answer below:
\( x_{n+1}=\square \)
Q:
17) The function \( A=A_{0} e^{-0.01155 x} \) models
the amount of a particular radioactive
material stored in a concrete vault, where
\( x \) is a number of years since the
material was put into the vault. Suppose
400 pounds of the material are initally
put into the vault. Ansuer the folloving
questions:
a) How many pounds will be left after
130 years? (Round to nearest whole number)
b) After how many yews will there be 50 pounds
remaining? (Round to newest whole number)
Q:
Approximate the area under the graph of \( f(x) \) and above the \( x \)-axis using \( n \) rectangles.
\( f(x)=2 x+3 \) from \( x=0 \) to \( x=2 ; n=4 \); use right endpoints
Q:
\begin{tabular}{l} Question \\ Use Newton's method to approximate the solution to the equation \( 7 \cos (x)=3 x+1 \). Use \( x_{0}=2 \) as your starting value \\ to find the approximation \( x_{2} \) rounded to the nearest thousandth. \\ Provide your answer below: \\ \\ \( x_{2} \approx \square \) \\ \hline\end{tabular}
Q:
3.1.2 \( \int \frac{-3 x}{\sqrt{x^{2}-9}} d x \)
3.1.3 \( \int \frac{1}{x^{2}-4} d x \)
Q:
Question
Use Newton's method to approximate the solution to the equation \( \sqrt{x+10}=4 x^{2}+3 x \). Use \( x_{0}=2 \) as your starting
value to find the approximation \( x_{2} \) rounded to the nearest thousandth.
Provide your answer below:
\( x_{2} \approx \square \)
Q:
Question
For the equation given below, one could use Newton's method as a way to approximate the solution. Find Newton's formula
as \( x_{n+1}=F\left(x_{n}\right) \) that would enable you to do so.
\[ \sin (x)=6 x-5 \]
Provide your answer below:
\( x_{n+1}=\square \)
Q:
\( \int _ { - 2 } ^ { 2 } \int _ { 0 } ^ { \sqrt { 4 } - x ^ { 2 } } ( x ^ { 2 } + y ^ { 2 } ) ^ { \frac { 3 } { 2 } } d y d x \)
Q:
Question
Use Newton's method to approximate the solution to the equation \( 9 \ln (x)=-6 x+8 \). Use \( x_{0}=3 \) as your starting value
to find the approximation \( x_{2} \) rounded to the nearest thousandth.
Provide your answer below:
\[ \]
\( x_{2} \approx \square \)
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