Answer:
By definition, the slope of a vertical line is undefined. Because the value of x is always equal to 4 it is never equal to 0 therefore there is no y-intercept.
Step-by-step explanation:
Solving the inequality 
we get 
Step-by-step explanation:
We need to solve the inequality:
Solving:
Adding -4 on both sides:
Divide both sides by -7 and reverse the inequality:
So, solving the inequality we get
Keywords: Solving inequalities
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Answer:
a. y= e raise to power y
c. y = e^ky
Step-by-step explanation:
The first derivative is obtained by making the exponent the coefficient and decreasing the exponent by 1 . In simple form the first derivative of
x³ would be 2x³-² or 2x².
But when we take the first derivative of y= e raise to power y
we get y= e raise to power y. This is because the derivative of e raise to power is equal to e raise to power y.
On simplification
y= e^y
Applying ln to both sides
lny= ln (e^y)
lny= 1
Now we can apply chain rule to solve ln of y
lny = 1
1/y y~= 1
y`= y
therefore
derivative of e^y = e^y
The chain rule states that when we have a function having one variable and one exponent then we first take the derivative w.r.t to the exponent and then with respect to the function.
Similarly when we take the first derivative of y= e raise to power ky
we get y=k multiplied with e raise to power ky. This is because the derivative of e raise to a constant and power is equal to constant multiplied with e raise to power y.
On simplification
y= k e^ky
Applying ln to both sides
lny=k ln (e^y)
lny=ln k
Now we can apply chain rule to solve ln of y ( ln of constant would give a constant)
lny = ln k
1/y y~= k
y`=k y
therefore
derivative of e^ky = ke^ky
Answer:
It's is A and D.
Step-by-step explanation:
Tan^2 theta cos 2theta
= (sin^2 theta / cos^2 theta )( 2 cos^2 theta - 1)
= 2 sin^2 theta - sin^2 theta / cos^2 theta
= 2 sin^2 theta - tan^2 theta.
Tan^2 theta cos 2theta
= ( 1 / cot^2 theta) * cos 2theta
= cos 2theta / cot^2 theta.
