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@mathwork

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Is there a way to memorize the unit circle without having to actually stare at it for hours? Like a mnemonic of some sort?
you can use your hand, but i just memorized the circle when i learned it. youβll see after a while that the sin, cos, and tan values only take on a set number of values. they just change signs and angles each quadrant
How can you tell the difference between a cusp and a corner?
https://math.stackexchange.com/questions/2429089/cusp-vs-corner-or-both
If the derivative of y=kx, where k is a constant, equals 4 when x=-1. What is the derivative of y=k (1-sqrt(x)) when x=4?
y = kx
dy/dx = k =Β 4
k = 4
y = k(1-sqrt(x)) = 4(1-sqrt(x)) = 4 - 4*x^(1/2)
dy/dx = 0 - 4*(1/2)*x^(-1/2) = -2/sqrt(x)
dy/dx(4) = -2/sqrt(4) = -2/2 = -1
I got this wrong on a test, and I was wondering how you would do it.
f(3+delx) = 5*(3+delx) = 15+5delx
f(3) = 5*3 = 15
lim as delx goes to 0 of [f(3+delx)-f(3)]/delx =
lim as delx goes to 0 of [15+5delx-15]/delx =
lim as delx goes to 0 of 5*delx/delx =Β
5*( lim as delx goes to 0 of delx/delx) =Β
5*1 = 5

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dx/x sqrt 25x^2+16
d/dx[sqrt(25x^2+16)]
=Β d/dx[(25x^2+16)^(1/2)]
= (1/2)*(25x^2+16)^(-1/2)*(2)*(25x) = 25x/(sqrt(25x^2+16))
Your dedication to help people is admirable! Thank you for taking time from your busy schedule to help us! I'm someone who, sadly, failed at math, but i never stopped seeing the beauty in it. It's very interesting, and i have much respect for people who deal with it.
thanks! ik i havent really been helping out a lot recently so im sorry for that. i stopped taking math courses as part of my curriculum (im an engineer) and im really focused on research lately. hope the blog still helps ppl!
math sux lol
jk its ok B)
math sux lol

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can u help me with this ? in an isosceles triangle PQR , PQ = (3x + y) cm and QR = (5y - x) cm . If PR = QR , find the perimeter , in cm , of the triangle PQR . thanks x
Perimeter = PQ + QR + PR = (3x+y) + (5y-x) + (5y-x) = (11y+x) cm
Hello agaaaain. Is this correct? :)
yep itβs correct! good job!

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I NEED YOUR HELP ONCE AGAIN :(
Am i going to the right way? Tysm.
@sempre-felice Your process is right, but you messed up the integral a little bit. Yes, I would expand the integral and separate it out, but you don't need u substitution and (e^x)^2 = (e^x)(e^x) = e ^(x+x) = e^(2x) not e^(x^2) So integral (e^x + 1)^2 dx = integral (e^(2x) + 2e^(x) + 1) dx = integral (e^(2x))dx + integral (2e^(x))dx + integral 1 dx = (e^(2x)/2) + (2e^(x)) + x + C