{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 08wHW2 - f x = 0 for x ∈ a b 3 Let f g a b → R Suppose...

This preview shows page 1. Sign up to view the full content.

MAT 125B Homework 2 M.Fukuda Please submit your answers at the discussion session on January 29 Tuesday. You can use theorems in the lecuture unless otherwise stated. When you do so write those statements clearly instead of quoting them by numbers. 1. Let f : [ a, c ] R and b [ a, c ]. Show that integraldisplay b a f ( x ) dx = integraldisplay c a f ( x ) dx + integraldisplay b c f ( x ) dx. You don’t have to prove this result from scratch. 2. Let f : [ a, b ] R and α, β R with α negationslash = β . Suppose f is continuous on [ a, b ] and α integraldisplay c a f ( x ) dx + β integraldisplay b c f ( x
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f ( x ) = 0 for x ∈ [ a, b ]. 3. Let f, g : [ a, b ] → R . Suppose that f is di±erentiable and non-decreasing on [ a, b ], and f ′ is continuous on [ a, b ], and that g is di±erentiable on [ a, b ] and g ′ is integrable on [ a, b ], and g is strictly positive on ( a, b ) but g ( a ) = g ( b ) = 0. Then, show that f is constant on [ a, b ] if and only if i b a f ( x ) g ′ ( x ) dx = 0 . 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online