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galina1969 [7]
3 years ago
12

Find all extrema in the interval 0 2pi if y=x+sinx

Mathematics
1 answer:
ale4655 [162]3 years ago
4 0
<span>Answer: y = x + sin(x) y' = 1 + cos(x) Setting y' to zero, we have: y' = 0 1 + cos(x) = 0 cos(x) = -1 x = pi, on the interval [0, 2pi] y'' = -sin(x) When x = pi, y'' = -sin(pi) = 0 Thus, we have an extremum at x = pi, but it is neither a local maxima nor a local minima. Notice as well that y' = 1 + cos(x) >= 1 for all real values of x. Thus, y is an increasing function. This implies that on the interval [0, 2pi], the absolute minima is at x = 0, where y = 0 + sin(0) = 0; and the absolute maxima is at x = 2pi, where y = 2pi + sin(2pi) = 2pi.</span>
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I've included two questions. Hopefully you can help me with both. Thanks!
lubasha [3.4K]

Answer:

  1.  value is 0; x-3 is a factor . . . . . . . . . . . . . .third choice

  2.  evaluates at x = -1; remainder is -11 . . . . first choice

Step-by-step explanation:

Dividing f(x) by (x -a) gives ...

  f(x)/(x -a) = g(x) +r/(x -a) . . . . some quotient and a remainder r

If we multiply this expression by (x -a), we see ...

  f(x) = (x -a)g(x) +r

so

  f(a) = (a -a)g(a) +r . . . . . evaluate the above equation at x=a

  f(a) = 0 +r

  f(a) = r . . . . . . . . . a statement of the remainder theorem

If r=0, then x-a is a factor of f(x) = (x-a)g(x).

___

1. We have "a" = 3, and f(3) = 0. Therefore (x-3) is a factor.

__

2. We have "a" = -1, and f(-1) = -11. Therefore the remainder from division by (x+1) is -11.

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4 years ago
Terri buys five and seven eighths ounces of chocolate chips. She uses four and four sixths ounces in a recipe. How many ounces o
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Answer:

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If (5⁴)m = 5 ¹²,what is the value of m<br> 2<br><br> 3<br><br> 5<br><br> 8
Lapatulllka [165]
The correct answer is:  [B]:  " 3 " .
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Note:  
_______________________________________________
The question asks:
_______________________________________________
If (5⁴)ᵐ  = 5¹² ;  then what is "m" ?

Note the following property of exponents:
________________________________________________
   (xᵃ)ᵇ = x⁽ᵃ*ᵇ⁾ ; a≠0 ; b ≠ 0 ;  

Then,  (5⁴)³ = 5⁽⁴ * ³⁾ = 5¹² .

So, "12 ÷ 4 = 3" .
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The answer is:  "m = 3" ; which is:  Answer choice:  [B] .
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