MAT 17B Lecture 4: Section 6.3 Applications of Integrals

Find the Laplace transform of the given function. (Express your answer in terms of s. Assume that s >o.) 1 3-1050 ro = ts s 2 10

Find f f"(x) = 6 + 6x + 24x2, ro-3, f(1) : 13

Instructor: Dr. Yunjiao Wang 1. Determine whether the following statements are true or false. (a) Suppose f(z) is a function of one variable f is continuous at z = 3 if f,(3) exists. (b) Suppose f( ) is afunction of more than one variable, where = (zi,--,Zn)/ (c) Suppose /(/) is a function of incre than one variable, whereェ= ( , ' ). f (d) Suppose /(Z) is a function of more than one variable, whereェ= (n, ), f (e) Suppose f(r) is a function of more than one variable, where i (rn). is continuous at if exist at fo for all i = 1, , n. is continuous at to if are continuous at ro for all i 1, n. is differentiable at i。if at are continuous at ro for all i 1, , n. is continuous at ro if f is differentiable at ro