Why is cos(arctan x) = 1 / root(1+x^2)
and sin(arctan x) = x / root(1+x^2)?
I would greatly appreciate help. I'm studying for physics and this came up in one of the solutions. Thank you.
If point P(m,2m) is 5 units from the line 12x+5y=1, m could equal
a. 43/11
b.-3
c.-65/22
d.5
e.3
The answer is E.
Explanation given in book:
- distance = abs(12(m) + 5(2m) -1) / root(144+25) = 5.
>>> m=3 or -32/11
I do not understand this explanation (of course finding m from...
Homework Statement
Differential equation: dx/dt = 1000 + 0.10x
x(0) = 1000
Solve the initial value problem for x as a function of t
Section of Exponential/Logistic growth; applications (population growth) ---- Intro-level calculus
Homework Equations...
Homework Statement
Finding Area Find the area of the region enclosed by the y-axis and the curves y=x^2 and y=(x^2+x+1)*e^(-x)
The problem is from intro-level calculus and it's from
Chapter 6: Differential Equations and Mathematical Modeling
Section 3: Integration by parts
Book...
Finding derivative question please...
How should I find the derivative of y = x^(e^x)?
I tried using the chain rule along with the power rule, coming out to:
(e^x) (e^x) (X^(e^x - 1))
If I had took the natural log of both sides and then used implicit differentiation, I would have...
well very many thanks I give you. Sorry, I am only at precalculus and just at the basic level, so I don't really know what happens when you multiply an equation by (x^2 + 1), but as I tried doing that it worked! The graph of the quintic equation looks very similar to my original cubic equation...
Would you please give one or two (or more, sorry hehehe) to help me?
How can you make up a polynomial that:
- crosses the x-axis at -2
- just touches the x-axis at 1 ("touch" as the graph y=x^2 would only touch, not cross, the x-axis)
- and is above the x-axis between -2 and 1.
I know...