Topic
Q:
11. \( \int x^{2}(1+2 x) d x \)
Q:
(a) Find the gradient of the curve \( \cos (4 x y)=\tan \left(x y^{2}\right)-3 y \) at the point where \( x=0 \).
(b) Given \( x^{2} y=\sin \left(2 x^{2}+\pi\right) \).
Show that \( 2 y\left(1+8 x^{4}\right)+4 x \frac{d y}{d x}+x^{2} \frac{d^{2} y}{d x^{2}}=4 \cos \left(2 x^{2}+\pi\right) \).
Q:
9. \( \int \frac{(x \sqrt{x}-3)^{2}}{x^{3}} d x \)
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.
\[ \ln (x)-9=-7 x \]
Sorry, that's incorrect. Try again?
\( x_{n+1}=\square \)
Q:
1. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the
functions:
(a) \( F(r)=\int_{0}^{r} \sqrt{x^{2}+4} d x \)
Q:
Question
Use Newton's method to approximate the solution to the equation \( \frac{5}{x-10}=x+6 \). Use \( x_{0}=-5 \) as your starting value
to find the approximation \( x_{2} \) rounded to the nearest thousandth.
Sorry, that's incorrect. Try again?
\[ x_{2} \approx \square \]
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
A. 11
B. 13
C. 17
D. 15
Q:
A certain tranquilizer decays exponentially in
the bloodstream and has a half-life of 22
hours. How long with it take for the drug
to decuy to \( 82 \% \) of the original dose?
a) step 1 : Find \( K \) (Round to four decimalpleas)
b) step 2 : Use \( k \) to determine how longlinhours)
it will take for the drug to decay to \( 82 \% \) of
the original dose. (Round to one decinalplace)
Q:
A certain tranquilizer decays exponentially in
the bloodstrean and has a half-life of 22
hours. How long with it take for the drug
to decuy to \( 82 \% \) of the original dose?
a) step 1 : Find K (Round to four decinal pleces)
b) step \( 2: \) Use \( k \) to determine how longlinhours)
it will take for the devg to decay to \( 82 \% \) of
the original dose. (Round to one decinalplace)
Q:
Question
Approximate the \( x \)-value of the local minimum value of the function given below. Use Newton's method with the specified
initial approximation \( x_{0} \) to find \( x_{2} \). Round your answer to the nearest thousandth.
\[ f(x)=\frac{5}{6} x^{3}+\frac{5}{2} x^{2}-5 x+2, \quad x_{0}=3 \]
Provide your answer below:
\[ \]
\( x_{2} \approx \square \)
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