Answer:
Take a look at the 'proof' below
Step-by-step explanation:
The questions asks us to determine the anti-derivative of the function f(x) = 4x^3 sec^2 x^4. Let's start by converting this function into integral form. That would be the following:
Now all we have to do is solve the integral. Let's substitute 'u = x^4' into the equation 'du/dx = 4x^3.' We will receive dx = 1/4x^3 du. If we simplify a bit further:
Our hint tells us that d/dx tan(x) = sec^2(x). Similarly in this case our integral boils down to tan(u). If we undo the substitution, we will receive the expression tan(x^4). Therefore you are right, the first option is an anti-derivative of the function f(x) = 4x^3 sec^2 x^4.
If it needs to be in decimal form it would be: y=0.25x-6
Fraction form would be: y=1/4x-6
Step-by-step explanation:
A) You're just plugging in an "x" into the given equation here, and you need 8. I'd go with numbers that divide into whole integers by 8 (e.g. -4, -2, 2, 4), write down the x, then "y" after plugging into the equation.
B) Plot the coordinates you got from the first problem.
C) Any linear function has the domain of all real numbers, meaning that you can plug in any "x" and it'll work. What if you have a rational (something in the denominator) function though and x is in the denominator? Well, if we plug in any number and divide by 8, it works, BESIDES 0. You cannot divide by zero, and we call this "undefined" in math. There is no definitive nor quantitative answer, it is simply "undefined" because you can't divide something by 0
BY USING MIDDLE TERM SPLITTING,
3y^2-(3y-2y)-2
(3y^2-3y)+(2y-2)
3y(y-1)+2(y-1)
(3y+2)(y-1)
HOPE THIS WILL HELP U