Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval.

Rivka Thorpe
2021-06-20
Answered

Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval.

You can still ask an expert for help

Alara Mccarthy

Answered 2021-06-21
Author has **85** answers

Polynomial and root functions are continuous over their domains.

Polynomials such as 3— x are continous for all real numbers, so it is contintious and also$\ge 0$ for the given interval.

The domains of root functions are the values for which the radicand (value inside the radical) is$\ge 0$ .

The composition of 3 — 2 and the root function will also be continuous ("theorem 9”) since both are continuous on their own.

$\sqrt{3-x}$

The ”2” can be considered a constant function which is also continuous. The product of two continuous functions is also continuous. So g(z) is eontintntis far the-siven interral.

Polynomials such as 3— x are continous for all real numbers, so it is contintious and also

The domains of root functions are the values for which the radicand (value inside the radical) is

The composition of 3 — 2 and the root function will also be continuous ("theorem 9”) since both are continuous on their own.

The ”2” can be considered a constant function which is also continuous. The product of two continuous functions is also continuous. So g(z) is eontintntis far the-siven interral.

asked 2021-01-31

Find a basis for the space of $2\times 2$ diagonal matrices.

$\text{Basis}=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

asked 2021-02-08

Let B be a 4x4 matrix to which we apply the following operations:

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

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What's the value of x when $\mathrm{sin}x=2$ and x is a complex number?

asked 2022-07-08

Contradiction in solving $\mathrm{sin}(z)=0$?

$\mathrm{sin}(z)=0$

${e}^{-i(x+iy)}={e}^{i(x+iy)}$

${e}^{-ix+y}={e}^{ix-y}$

${e}^{ix-y+ix-y}=1$

${e}^{2ix-2y}={e}^{0}$

$\Rightarrow 2ix-2y=0$

ix=y

z=x+xi

but, $2i(x+iy)=2iz=0$

$\Rightarrow z=0,z=2\pi n$

※ ?

$\mathrm{sin}(z)=0$

${e}^{-i(x+iy)}={e}^{i(x+iy)}$

${e}^{-ix+y}={e}^{ix-y}$

${e}^{ix-y+ix-y}=1$

${e}^{2ix-2y}={e}^{0}$

$\Rightarrow 2ix-2y=0$

ix=y

z=x+xi

but, $2i(x+iy)=2iz=0$

$\Rightarrow z=0,z=2\pi n$

※ ?

asked 2022-04-29

I can't find a way to solve this:

${\int}_{\frac{\pi}{2}}^{\pi}\sqrt{8{\mathrm{sin}}^{2}\left(t\right){\mathrm{cos}}^{2}\left(t\right)}dt$

asked 2021-09-20

Solve the polynomial inequality graphically.

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$\mathrm{cot}(2{\mathrm{cot}}^{-1}t)$ simplifies to?