Search & Filtering
Let F(x)=∫
t−3
t
2+7
for − ∞ < x < ∞
x
(a) Find the value of x where F attains its minimum value.
(b) Find intervals over which F is only increasing or only decreasing.
(c) Find open intervals over which F is only concave up or only concave down.
(a) Evaluate∫[
𝒙/(𝒙^2+𝟏)^(1/2)𝒅𝒙.
(b) Use MATLAB to generate some typical integral curves of 𝑓(𝑥) =
𝒙/(𝒙^2+𝟏)^(1/2)𝒅𝒙over the interval (−5,5).
Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 − 2xy + y2, (1, 5, 16) with maple lab please
The functions f and g are defined by f(x) =1/(1-3x) and g(x) =log1/3(3x-2)-log3(x) respectively
1. Write down the sets Df (ehe domain of f) and Dg (the domain of g)
2. Solve the inequality f(x) > 2 for x\is in∈ Df
3. Solve the inequality f(x) ≥ 2 for x\is in∈ Dg
Hint: Use the change of base formula
Determine the length of the curve 𝑥 = 𝑦^2 /2 for 0 ≤ 𝑥 ≤ 1/2 . Assume 𝑦 positive.
Determine the volume of the solid/ring obtained by the region bounded by
𝑦=2√𝑥−1and 𝑦=𝑥−1 about line x= -1 using shell method
DM. solve the recurrence t(n)=(t(n/2)^2) assuming t(1)=1
DM. list the ordered pairs in the equivalence relations R induced by these partitions of p { {1} , {3} , { 2,4,5,6} rt he set of { 1,2,3,4,5,6}
If x is positive show that. x>log(1+x)>x-(x^2/2)
Using Taylor's theorem prove that. x-(x^3/6)<sinx<x-(x^3/6)+(x^5/120)
