Tobias Ali
2020-11-09
Answered

Sketch a graph of the function. Use transformations of functions whenever possible.
$f\left(x\right)=\text{}\frac{1}{{(x\text{}-\text{}1)}^{3}}$

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mhalmantus

Answered 2020-11-10
Author has **106** answers

Step 1 First graph function

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Write the given matrix equation as a system of linear equations without matrices. $\left[\begin{array}{cc}3& 0\\ -3& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}6\\ -7\end{array}\right]$

asked 2022-02-26

Show that

$-2\le \mathrm{cos}\theta (\mathrm{sin}\theta +\sqrt{{\mathrm{sin}}^{2}\theta +3})\le 2$

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How do you solve $\frac{2}{3\sqrt{2}}=\mathrm{cos}\left(\frac{x}{2}\right)$

asked 2021-08-15

Find a vector equation and parametric equations for the line segment that joins P to Q.

P(0, - 1, 1), Q(1/2, 1/3, 1/4)

P(0, - 1, 1), Q(1/2, 1/3, 1/4)

asked 2022-03-16

Can someone please help me with this question:

$\int \frac{16}{1-\mathrm{cos}8x}dx$

asked 2022-05-23

Find the exact value of ${\mathrm{sin}}^{-1}(-\frac{\sqrt{3}}{2})$ and the like.

a. ${\mathrm{sin}}^{-1}(-\frac{\sqrt{3}}{2})$

b. ${\mathrm{cot}}^{-1}(-1)$

c. ${\mathrm{sec}}^{-1}\left(\frac{2}{\sqrt{3}}\right)$

d. ${\mathrm{cos}}^{-1}(-\frac{\sqrt{2}}{2})$

e. ${\mathrm{tan}}^{-1}(-\sqrt{3})$

a. ${\mathrm{sin}}^{-1}(-\frac{\sqrt{3}}{2})$

b. ${\mathrm{cot}}^{-1}(-1)$

c. ${\mathrm{sec}}^{-1}\left(\frac{2}{\sqrt{3}}\right)$

d. ${\mathrm{cos}}^{-1}(-\frac{\sqrt{2}}{2})$

e. ${\mathrm{tan}}^{-1}(-\sqrt{3})$

asked 2022-07-22

How to find all points for which the tangent line of a parametric equation (x, y, z) passes through a point

For the function

$\overrightarrow{x}(t)=\left(\begin{array}{c}2t+3\\ 2-t\\ {t}^{3}-2{t}^{2}+t\end{array}\right)t\ge 0$

Find all points $\overrightarrow{x}({t}_{0})$ for which the tangent line passes through the point (1, 3, 0).

I understand how I would go about solving the problem if I had a normal polynomial function or only x and y values. However, with x, y, and z values I am not sure how to approach the question.

I know that the derivative of the function is

${\overrightarrow{x}}^{\prime}(t)=\left(\begin{array}{c}2\\ -1\\ 3{t}^{2}-4t+1\end{array}\right)$

Would I then have to find the equation of the tangent line and use that with the given point to find the other points?

For the function

$\overrightarrow{x}(t)=\left(\begin{array}{c}2t+3\\ 2-t\\ {t}^{3}-2{t}^{2}+t\end{array}\right)t\ge 0$

Find all points $\overrightarrow{x}({t}_{0})$ for which the tangent line passes through the point (1, 3, 0).

I understand how I would go about solving the problem if I had a normal polynomial function or only x and y values. However, with x, y, and z values I am not sure how to approach the question.

I know that the derivative of the function is

${\overrightarrow{x}}^{\prime}(t)=\left(\begin{array}{c}2\\ -1\\ 3{t}^{2}-4t+1\end{array}\right)$

Would I then have to find the equation of the tangent line and use that with the given point to find the other points?