Differentiate y= In ( 2cot²x )
Differentiate y= In ( 2cot²x )
y=(x-1)√x²-2x+2
If (𝑥, 𝑦, 𝑧) =𝑋^ 2 𝑌 − 2 𝑌^ 2𝑍 ^3, find ∇𝑓 at the point (1, −1,2)
the sum of two numbers is 4. find the minimum value of the sum of their cubes.
A. Tell whether each given function has a solution on the indicated closed interval. Prove using the Intermediate value theorem.
1. f(x)=3x²+2x²;[-1,1]
2. f(x)= 2-x²/x²;[-3,-1]
B. Sketch the graph of the following functions and then find the absolute extreme values of each of the given interval.
1.f(x)=√x²-25;[5,10]
2. f(x)=-1/x²;[0.5,2]
C. A restaurant's profit function (in hundreds) for hamburgers is given by the function P such that P(x)=1.22x-x²/30,000-4,000,where 0≤x≤20,000.
1. How many hamburgers does the restaurant need to sell to yield the maximum profit?
2. What is the maximum profit from the sale of hamburger ?
B. Sketch the graph of the following functions and then find the absolute extreme values of each of the given interval.
1.f(x)=3-2/5x;[-4,0]
2.f(x)=x-3/4+x;[-3,1]
C. Let f(x)=2x+1. Determine if the Intermediate value theorem applies to f on the closed interval [-3,4]for k=1.
using ϵ−δ definition, show that
lim x→2 (1/2 x2 - x + 1)
Using the definition of limit at infinity or infinite limits, prove that
a) lim𝑥 → 3 1/ (𝑥 − 3) 2 = ∞
Using Intermediate Value Theorem, show that
x2 = √𝑥 + 1 has a root in (1,2)