[x] is known as the greatest integer function. its output is the greatest integer which is less than or equal to x. Therefore \(\displaystyle{f{{\left({2.1}\right)}}}={\left[{\left[{2.1}\right]}\right]}={2}.{f{{\left({2.1}\right)}}}={2}\)

asked 2021-10-16

Use the value of the trigonometric function to evaluate the indicated functions. \(\displaystyle{\sin{{t}}}=\frac{{4}}{{5}},{\sin{{\left({t}+\pi\right)}}}\)

asked 2021-10-14

At what points is the direction of fastest change of the function \(\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{2}}+{y}^{{2}}-{4}{x}-{8}{y}\) is i+j.

asked 2021-10-29

Find the inverse the function and the domain and the range of f and \(\displaystyle{f}^{{-{1}}}\), if the function is \(\displaystyle{f{{\left({x}\right)}}}={2}\frac{{x}}{{{x}+{5}}}\) and it's one-to-one.

asked 2021-10-31

\(\displaystyle{C}{\left({x}\right)}={5},{000}+{20}{x}-\frac{{1}}{{4}}{x}^{{2}}\)

is a cost function.

Calculate the marginal average cost when 20 (a), use your result to estimate the total cost when x=21 (b) and calculate the percentage error between this estimate and the actual cost when x=21 (c).

is a cost function.

Calculate the marginal average cost when 20 (a), use your result to estimate the total cost when x=21 (b) and calculate the percentage error between this estimate and the actual cost when x=21 (c).

asked 2021-10-28

Write the first trigonometric function in terms of the second for \(\displaystyle\theta\) in the given quadrant

\(\displaystyle{\tan{\theta}},\ {\cos{\theta}};\ \theta\ \text{ in Quadrant II}\)

\(\displaystyle{\tan{\theta}},\ {\cos{\theta}};\ \theta\ \text{ in Quadrant II}\)

asked 2021-10-14

Suppose \(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}{\quad\text{and}\quad}{g{{\left({x}\right)}}}=\sqrt{{{x}-{5}}}\), to find:

1. (fog)(x)

2. Domain of (fog)(x)

3. (gof)(x)

4. Domain of (gof)(x)

1. (fog)(x)

2. Domain of (fog)(x)

3. (gof)(x)

4. Domain of (gof)(x)

asked 2021-10-26

if x=2 , f(x)=1

if x=3 , f(x)=4

if x=5 , f(x)=-2

if x=8 , f(x)=3

if x=13 , f(x)=6

f is twice variable for all real numbers.

1. Find f'(4)

2. Approximate \(\displaystyle{\underset{{{2}}}{{\int}}}^{{13}}{f}'{\left({x}\right)}{\left.{d}{x}\right.}\)

2. Find the value of \(\displaystyle{\underset{{{2}}}{{\int}}}^{{8}}{\left({3}-{f}'{\left({x}\right)}\right)}{\left.{d}{x}\right.}\)

if x=3 , f(x)=4

if x=5 , f(x)=-2

if x=8 , f(x)=3

if x=13 , f(x)=6

f is twice variable for all real numbers.

1. Find f'(4)

2. Approximate \(\displaystyle{\underset{{{2}}}{{\int}}}^{{13}}{f}'{\left({x}\right)}{\left.{d}{x}\right.}\)

2. Find the value of \(\displaystyle{\underset{{{2}}}{{\int}}}^{{8}}{\left({3}-{f}'{\left({x}\right)}\right)}{\left.{d}{x}\right.}\)