Find ${\vec{f}} \ '(t)$ for the vector function, and state the domain of each derived function.

$$\vec{f}(t)=3^{2 t^2} \bar{i}+\dfrac{2 t-3}{2 t+4} \hat{j}$$

Graph by hand the standard normal distribution by using the formula derived in the Previous Exercise. Let $\pi \approx 3.14$ and $e \approx 2.718$. Use $X$ values of $-2,-1.5,-1,-0.5,0,0.5$, $1,1.5$, and $2.$ (Use a calculator to compute the $y$ values.)

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How can you prevent cystitis and urethritis?

Identifying the Number of Nouns and Pronouns. Label each of the following words as singular or plural. he

Describe the challenges in identifying teratogens.

A Taylor polynomial centered at 0 will be used to approximate the cosine function. Find the degree of the polynomial required to obtain the desired accuracy over the indicated interval.

Maximum Error: 0.001, Interval: [-0.5,0.5]

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Rewrite each of the following sentences to correct a misplaced or dangling modifier.

Example 1. At the age of six, my father decided that I was ready for my first camping trip. $\underline{\text{When I was six my father decided that I was ready for my first camping trip.}}.$

8. Always check your work after you have finished for accuracy. $\underline{\phantom{\text{The horse with the sllvery mane and white tall was chosen by the photographer.}}}$

Reduce $[A | I]$ to find $A^{−1}$. In each case, check your calculations by multiplying the given matrix by the derived inverse.

$$\left[\begin{array}{lll} 1 & 3 & 5 \\ 0 & 1 & 4 \\ 0 & 2 & 7 \end{array}\right]$$

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Which word could best replace derived?

(A) predicted (B) ignored (C) hidden (D) received

The period of a pendulum is given by $T = 4 \sqrt { \frac { \ell } { g } } \int _ { 0 } ^ { \pi / 2 } \frac { d \theta } { \sqrt { 1 - k ^ { 2 } \sin ^ { 2 } \theta } } = 4 \sqrt { \frac { \ell } { g } } F ( k )$, where $\ell$ is the length of the pendulum, $g \approx 9.8 \mathrm { m } / \mathrm { s } ^ { 2 }$ is the acceleration due to gravity, k=sin $\left( \theta _ { 0 } / 2 \right)$, and $\theta _ { 0 }$ is the initial angular displacement of the pendulum (in radians). The integral in this formula F(k) is called an elliptic integral, and it cannot be evaluated analytically.

Approximate F(0.1) by expanding the integrand in a Taylor (binomial) series and integrating term by term.

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