SOLUTION: Really need the step by step solution to these questions 1. What is the tangent line of y = cos x at x = π/4? 2. What is the derivative of (5x + 2)(x^3 + 4x)? 3. Cons

Algebra ->  Matrices-and-determiminant -> SOLUTION: Really need the step by step solution to these questions 1. What is the tangent line of y = cos x at x = π/4? 2. What is the derivative of (5x + 2)(x^3 + 4x)? 3. Cons      Log On


   

Question 965782: Really need the step by step solution to these questions
1. What is the tangent line of y = cos x at x = π/4?
2. What is the derivative of (5x + 2)(x^3 + 4x)?
3. Construct an f(x) such that lim f(x) = ∞ but lim (x-3)f(x) = 0
x→3 x→3
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.The slope of the tangent line is the value of the derivative at the point of interest.
y=cos%28x%29
dy%2Fdx=-sin%28x%29
m=dy%2Fdx=-sin%28pi%2F4%29=-sqrt%282%29%2F2
Find the value of y at x=pi%2F4.
y=cos%28pi%2F4%29
y=sqrt%282%29%2F2
Now use the point slope form of a line,
y-sqrt%282%29%2F2=-%28sqrt%282%29%29%2F2%28x-pi%2F4%29
y-sqrt%282%29%2F2=-%28sqrt%282%29%2F2%29x-%28pi%2Asqrt%282%29%29%2F8
highlight%28y=-%28sqrt%282%29%2F2%29x%2B%28sqrt%282%29%2F2%29%281-pi%2F4%29%29
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2. dy%2Fdx=%285x%2B2%29%283x%5E2%2B4%29%2B%28x%5E3%2B4x%29%285%29
dy%2Fdx=%2815x%5E3%2B6x%5E2%2B20x%2B8%29%2B%285x%5E3%2B20x%29
dy%2Fdx=20x%5E3%2B6x%5E2%2B40x%2B8
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3. f%28x%29=1%2F%28x-3%29 for (-infinity,3)U(3,infinity) and
f%28x%29=0 for x=3