Anonym
2021-08-07
Answered

Use a graphing calculator to examine the graphs of the following functions. Determine ⋅⋅ the degree of the polynomial ⋅⋅ the leading coefficient ⋅⋅ the end behavior of the polynomial function ⋅⋅ the maximum number of zeros ⋅⋅ the maximum number of turning points (relative maxima and minima) $a.f\left(x\right)=\frac{1}{2}{x}^{2}+2x\text{}b.f\left(x\right)=x{(x+1)}^{2}{(x-1)}^{2}\text{}c.f\left(x\right)={x}^{3}-{x}^{2}+31x+40$

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un4t5o4v

Answered 2021-08-08
Author has **105** answers

Step 1

a.Degree:2(highest-degree monomial is

Leading coefficient:

End behavior:

Maximum number of zeros: 2(same as degree)

Maximum number of turning points: 1(one less than degree)

Step 2

b. Degree:5(product of 5 linear factors)

Leading coefficient: 1(product of coefficient of x terms)

End behavior: y

Maximum number of zeros: 5(same as degree)

Maximum number of turning points: 4 (one less than degree)

Step 3

c. Degree: 3 (degree of highest-degree monomial

Leading coefficient: 1(coefficient of highest-degree monomial)

End behavior:

Maximum number of zeros: 3 (same as degree)

Maximum number of turning points: 2 (one less than degree)

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Let $f\left(x\right)=\mathrm{sin}\left(2x\right)$

Prove or disprove there are a sequnce of polynomials${P}_{n}\left(x\right)$ which convenes to $f\left(x\right)$ uniformly on $(0,\mathrm{\infty})$ .

Prove or disprove there are a sequnce of polynomials

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Proof that:

$\mathrm{cos}}^{2}{10}^{\circ}+{\mathrm{cos}}^{2}{50}^{\circ}-{\mathrm{sin}40}^{\circ}{\mathrm{sin}80}^{\circ}=\frac{3}{4$

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please provide answer for this question
Show that the vector field by ⃗= (x^2+4yz)̂+ (y^2+4zx)̂+ (z^2+4xy) ̂ is irrotational. Hence find the scalar potential.

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Find the number of real solutions on an interval $(0,\pi )$ of this equation

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I am trying to compute the integral

$\begin{array}{}\text{(1)}& {\int}_{0}^{\pi /3}\frac{x}{\mathrm{cos}(x)}\phantom{\rule{thinmathspace}{0ex}}dx\end{array}$

$\begin{array}{}\text{(1)}& {\int}_{0}^{\pi /3}\frac{x}{\mathrm{cos}(x)}\phantom{\rule{thinmathspace}{0ex}}dx\end{array}$

asked 2022-01-29

How do you integrate $\int \frac{\mathrm{cos}\left(4x\right)}{\mathrm{cos}\left(x\right)}dx$

I tried using trigonometric formulas for turning it into$2\int \frac{{\mathrm{cos}}^{2}\left(2x\right)}{\mathrm{cos}\left(x\right)}dx-\int \frac{1}{\mathrm{cos}\left(x\right)}dx$ and can solve the second one, but still no idea of how to proceed with $\int \frac{{\mathrm{cos}}^{2}\left(2x\right)}{\mathrm{cos}\left(x\right)}dx$ .

I tried using trigonometric formulas for turning it into

asked 2021-08-16

For each of the following functions f (x) and g(x), express g(x) in the form $a:f(x+b)+c$ for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map $f\left(x\right)\text{}\to \text{}g\left(x\right).\left(a\right)\left(i\right)$

$f\left(x\right)={x}^{2},g\left(x\right)=2{x}^{2}+4x$

$\left(ii\right)f\left(x\right)={x}^{2},g\left(x\right)=3{x}^{2}-24x+8$

$\left(b\right)\left(i\right)f\left(x\right)={x}^{2}+3,g\left(x\right)={x}^{2}-6x+8$

$\left(ii\right)f\left(x\right)={x}^{2}-2,g\left(x\right)=2+8x-4{x}^{2}$