Answer:
dy/dx = (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]
Step-by-step explanation:
y = (x^2 - 3)^sinx
ln y = ln (x^2 - 3)^sinx
ln y = sin x * ln (x^2 - 3)
1/y * dy/dx = sin x * {1 / (x^2 - 3)} * 2x + ln(x^2 - 3) * cos x
1/y dy/dx = 2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)
dy/dx = [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)] * y
dy/dx = (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]
Answer: The numerator and denominator degrees of freedom (respectively) for the critical value of F are <u>4</u> and<u> 118 .</u>
Step-by-step explanation:
We know that , for critical value of F, degrees of freedom for numerator = k-1
and for denominator = n-k, where n= Total observations and k = number of independent variables.
Here, Numbers of independent variables(k) = 5
Total observations (n)= 123
So, Degrees of freedom for numerator = 5-1=4
Degrees of freedom for denominator =123-5= 118
Hence, the numerator and denominator degrees of freedom (respectively) for the critical value of F are <u>4</u> and<u> 118 .</u>
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The correct answers are:</span><span>
(1) The vertical asymptote is x = 0
(2) The horizontal asymptote is y = 0
</span><span>
Explanation:</span><span>(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.
Rational Function = g(x) = </span></span>
<span>
Denominator = x = 0
Hence the vertical asymptote is x = 0.
(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:
Given function = g(x) = </span>
<span>
We can write it as:
g(x) = </span>
<span>
If power of x in numerator is less than the power of x in denomenator, then the horizontal asymptote will be y=0.
If power of x in numerator is equal to the power of x in denomenator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denomenator).
If power of x in numerator is greater than the power of x in denomenator, then there will be no horizontal asymptote.
In above case, 0 < 1, therefore, the horizontal asymptote is y = 0
</span>
3/4 equals .75, and 60% equals .60. Therefore, we can set up an equation. .75=.60x, where x is the number we are looking for.
Divide each side by .60 to get the variable by itself. .75/.60= 1.25.
Hope this helped!!! :)