Demonstrate using regression functions by explaining what a regression function is and the factors which should be considered when interpreting results.
Integration: Standard Partition, Integrable over a Range
Questions on integration, see attachment.
Differentiation : Existence of Solutions
I want to prove, for the numbers a and b, that the following equation has exactly three solutions if and only if 4a^3 + 27b^2 < 0: x^3 + ax + b = 0, x in R
Real Analysis : Differentiation
If I let the function f:R->R have two derivatives with f(0)=0 and f'(x) <= f(x) for all x in R. Is f(x)=0 for all x in R?
Real Analysis: Differentiation
If I let the function f:R->R have two derivatives with f(0) = 0 and f'(x) <= f(x) for all x in R. Is f(x) = 0 for all x in R
If I say that the function f:R->R has two derivatives, with f(0) = f'(0) = 0 and the absolute value of f"(x) is less than or equal to one, if the absolute value of x is less than or equal to 1. How can I prove that: f(x) <= 1/2 if x <= 1
fundamental differential equation analysis
If I let I be an open interval containing the point x. (x not) and suppose that the function f:I->R has two derivatives. How can I prove that lim as h->0 (f(x.+h) - 2f(x.) + f(x.-h))/ h^2 = f"(x.)
1a.)Is y=x^4 a single- or multi-valued function? b.)Is y=f(x)=x^2+4x an even, odd, or neither function? c.)What is the inverse function of y=x^4 d.)What is the inverse function of (b.),y=x^2+4x? e.)Is the inverse function from (d.), odd, even, or neither?
5. (a) Find derivatives of these functions chosing appropriate methods.. (See attached file)
Let X be a metric space and x0 in X. Define a function f: X --> R (all real numbers) by f(x) = d(x,x0). Show that f is continuous. HINT: Prove the variant of the triangle inequality which says |d(x,z)-d(y,z)|< d(x,y) for any x,y,z in X
